Answer: John is 29 years old and Jane is 36 years old.
Step-by-step explanation:
There are many parts to this problem, so let's start by defining John as x and Jane as y.
We know that the sum of their age 10 years ago was 55, which gives us x+y-10=55. The reason we put -10 is because of 10 years ago. If you think about it in terms of now, 10 years back is 55, so now they would be 65 years old. So we can have either x+y-10=55 or x+y=65. For simplicity, I will use x+y=65.
We also know that John is 7 years younger than Jane, which gives x=y-7.
Luckily, we have x defined for us, so we can directly substitute that into our equation.
[tex](y-7)+y=65[/tex] [combine like terms]
[tex]2y-7=65[/tex] [add both sides by 7]
[tex]2y=72[/tex] [divide both sides by 2]
[tex]y=36[/tex]
Now we know that y=36, we can plug that into either equations to find x.
[tex]x+36=65[/tex] [subtract both sides by 36]
[tex]x=29[/tex]
This concludes that John is 29 years old and Jane is 36 years old.
9/10 - 3/10
?????…..
Answer:
Step-by-step explanation:
9 - 3 = 6
6/10 = 3/5
Answer:
6/10 and/or 3/5(this is the answer simplified
Step-by-step explanation:
Subtract: 9/10 - 3/10
= 9 - 3/10
= 6/10
= 2 · 3/ 2 · 5
= 3/5
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 10) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 3/5. In other words - nine tenths minus three tenths is three fifths.
You have $9 to spend on lip balm and hand sanitizer. The equation $1.5x+2.5y=9$ represents this situation, where x is tubes of lip balm and y is bottles of hand sanitizer. How many tubes of lip balm can you buy when you do not buy any bottles of hand sanitizer?
Answer:
6 tubes of lip balm
Step-by-step explanation:
We can start solving this problem by isolating the variable x.
Given the equation 1.5x + 2.5y = 9, and we know that y = 0 (because we're not buying any bottles of hand sanitizer), we can substitute this into the equation:
1.5x + 2.5(0) = 9
Simplifying this, we get:
1.5x = 9
To solve for x, we can divide both sides of the equation by 1.5:
x = 9/1.5
x = 6
So we can buy 6 tubes of lip balm if we do not buy any bottles of hand sanitizer
Find the distance between the two points rounding to the nearest
(if necessary)
tenth
(1, -6) and (-8, -4)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 1~~)^2 + (~~-4 - (-6)~~)^2} \implies d=\sqrt{(-8 -1)^2 + (-4 +6)^2} \\\\\\ d=\sqrt{( -9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }\implies d\approx 9.22[/tex]
The difference between the two groups compared will have more significance as the p-value becomes __________. The difference between the two groups compared will have more significance as the t-value becomes __________.
The significance of the difference between the two groups under comparison will increase as the p-value decreases. The significance of the difference between the two groups under comparison will increase as the t-value rises.
If there is a significant difference between two groups, what does that mean?A difference that is "statistically significant" does not necessarily have to be "large, important, or significant in terms of the utility of the finding"; it simply means that there is statistical evidence that there is a difference.
When the p-value exceeds the significance level, what does that mean?In general, when the null hypothesis H0 is true, our sample results could have happened by random chance alone when the p-value is "high" (i.e. greater than or equal to the significance level).
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What is an unsolvable equation?
1. The Riemann Hypothesis Equation
Select all of the equations below in which a is directly proportional to b.
a=b²
b
= 1/1/20
a=
2
a= ²
b
a=2b
a=b+2
The equations which show direct proportion between a and b are:
a=2b and a=b/2.
What is direct proportion?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol, ∝. In fact, the same symbol is used to represent inversely proportional, the matter of the fact that the other quantity is inverted here.
Example: x and y are two quantities or variables which are linked with each other directly, then we can say x ∝ y. When we remove the proportionality symbol, the ratio of x and y becomes equal to a constant, such as x/y = C, where C is a constant.
Given, two variables a and b
If two variables a and b are in direct proportion
then,
a/b = constant.
1. a = b²
a/b = b
which is not constant
⇒ a is not in direct proportion with b.
2. a = 2b
a/b = 2
which is constant
⇒a is in direct proportion with b.
3. a = b/2
a/b = 1/2
which is constant
⇒ a is in direct proportion with b.
4. a=b+2
a/b = 1+2/b
which is not constant
⇒ a is not in direct proportion with b.
5. a = 2/b
ab = 2
⇒a is inversely proportional to b.
Hence, In equation a=2b and a=b/2, a is directly proportional to b.
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simplify 2√12+3√48-√75
Answer:
11√12
Step-by-step explanation:
√12 = 2√3
2√12
= 2 * 2√3
= 4√3
√48 = 4√3
3√48
= 3 * 4√12
= 12√12
√75 = 5√3
2√12 + 3√48 - √75
= 4√3 + 12√12 - 5√12
= 16√12 - 5√12
= 11√12
Answer: My answer is 11√3
Step-by-step explanation:
Pull terms out from under the radical, assuming positive real numbers.
Exact Form:
11√3
Decimal Form:
19.05255888…
What is the formula for directed line segment?
The formula for a directed line segment is A = (x2 - x1, y2 - y1). It is a vector equation, meaning that it describes the direction and magnitude of a line segment, rather than its endpoint coordinates.
A directed line segment is a line segment with a starting point and an ending point, where the direction of the line can be described in terms of its magnitude and direction. To calculate the directed line segment, first calculate the difference between the x-coordinates of the start and end points, and then calculate the difference between the y-coordinates of the start and end points. The result is the vector A, which describes the magnitude and direction of the line segment.
For example, consider a line segment with start point (1, 2) and end point (4, 6). To calculate the directed line segment, first calculate the difference between the x-coordinates of the start and end points (4 - 1 = 3). Then, calculate the difference between the y-coordinates of the start and end points (6 - 2 = 4). The result is the vector A = (3, 4). This vector describes the magnitude and direction of the line segment, with the magnitude being the length of the line segment, and the direction being the direction from the start point to the end point.
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please give a step by step explanation for this question
Answer:
[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]
Step-by-step explanation:
The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].
[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]
We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].
Now add these equations together to get our equation.
[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]
Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].
=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]
4
Drag each option to the correct location on the image.
Match the expenses to their respective categories.
Need
tuition and fees
staple foods
Want
Lamborghini
vacation
lavish wedding
Answer:
NEED:
Tuition and Feesstaple foodsWANT:
VacationLamborghini Lavish WeddingStep-by-step explanation:
Right on Plato! <3
Have a wonderful day!
The needs listed are tuition and fees and staple foods, while the wants are a vacation, a Lamborghini, and a lavish wedding.
The listed needs and wants reflect different aspects of a person's life and priorities. "Tuition and Fees" and "Staple Foods" are necessities that are essential for a person's survival and well-being.
On the other hand, "Vacation," "Lamborghini," and "Lavish Wedding" are desires that are often seen as luxury items or experiences. While having wants is normal and human, it is important to understand that not all wants can be fulfilled, and it is equally important to prioritize needs over wants. Having a balanced approach to spending, budgeting, and financial planning can help ensure that both needs and wants can be met in a sustainable manner.
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2. A recent study of 35 students determined that the mean number of hours per week they played video games was 16.6 hours. The standard deviation of the population was 2.8 hours. Find a 95% confidence interval of the population mean.
According to a recent study of 35 students,Population-wide, there was a 2.8-hour standard deviation. 16.60 is the population mean's 95% confidence interval.
What means 95% confidence interval?A Confidence Interval is a zone created using sampled data from a population (sample space) that has a fixed size and follows a specific probability distribution. The interval is built to include a selected population statistic with a certain probability. A range of values above and below the point estimate, within which the true value in the population is likely to reside with 95% confidence, is known as a 95% confidence interval. 5% of the time, the true result might not fall inside the confidence interval.A confidence interval that includes the value of no difference between treatments denotes that there is no statistically significant difference between the therapy under consideration and the control.The result is that P([sample mean] - margin of error [sample mean] + margin of error) = 0.95.To learn more about confidence interval refer to :
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Is there a triangle whose sides have length 10.2 cm 5.8 cm and 4.5 cm justify the answer?
Yes, a triangle whose sides have lengths 10.2 cm, 5.8 cm and 4.5 cm is possible.
As we know if these sides form a triangle, then
the sum of two sides > the third side
Now, the sum of 10.2 cm and 5.8 cm = 16 cm > 4.5 cm
The sum of 5.8 cm and 4.5 cm = 10.3 cm > 10.2 cm
The sum of 10.2 cm and 4.5 cm = 14.7 cm > 5.8 cm
Here the sum of the two sides is greater than the third side in all three cases.
Therefore a triangle whose sides are 10.2 cm, 5.8 cm and 4.5 cm is possible.
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Write an equation of the line that passes through the points (-7,-3) and (8, -3)
y=
Answer:
y = - 3
Step-by-step explanation:
Call the line y = a + bx (d)
Since d go through (-7;-3) so -7 = a - 3b (1)
Since d go through (8;-3) so 8 = a - 3b (2)
From (1) and (2), we have equations: [tex]\left \{ {{a - 3b = -7} \atop {a - 3b = 8}} \right.[/tex]
Solve the equations, we have [tex]\left \{ {{a = 0} \atop {b = -3}} \right.[/tex]
Which angle measures are correct? Select three options.
O m 2= 125°
m 3 = 55°
O m 8= 55°
O m 12= 100°
O m14 = 100°
Answer:
Step-by-step explanation:
analyze the graph, we found ∠1=∠5,∠2=∠6,
one.because ∠5+∠6=180, so ∠2=∠6=180-∠5=180-55=125
two.∠3=∠2=125
three.∠8=∠5=55
four.∠12=∠9=80
five.∠14=∠10=180-∠9=100
so, the three options are ∠2,∠8,∠14
For what value of k is the system of equations KX 3y K 2 12x Ky K inconsistent?
The system of equations is inconsistent for any value of k.
If we subtract the first equation from the second one, we get 0 = 12x, which is inconsistent no matter what value k is. This means that the system of equations has no solution and is therefore inconsistent.
The system of equations KX + 3y = K + 2 and 12x + Ky = K is inconsistent for any value of k. This is because when we subtract the first equation from the second one, we get 0 = 12x, which is an inconsistent equation no matter what value k is. This means that the system of equations has no solution and is therefore inconsistent. No matter what value we assign to k, the equations cannot be solved simultaneously and so the system of equations is inconsistent.
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Your grandmother has given you some money, and now you plan to save what she has given you along with a certain amount of money each week. After 17 weeks, you have $570, and after 29 weeks, you have $822. a) Find an equation (in slope-intercept form) of the amount of money saved after × weeks.
An equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.
What is the slope intercept form?The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.
The standard form of the slope intercept form is y=mx+c.
Given that, after 17 weeks, you have $570, and after 29 weeks, you have $822.
Here, (17, 570) and (29, 822)
Substitute (x₁, y₁)=(17, 570) and (x₂, y₂)=(29, 822) in m=(y₂-y₁)/(x₂-x₁)
= (822-570)/(29-17)
= 252/12
= 21
Substitute, m=21 and (x, y)=(17, 570) in y=mx+c, we get
570=21×17+c
570=357+c
c=213
Substitute, m=21 and c=213 in y=mx+c, we get
y=21x+213
Therefore, an equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.
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A population of 210,000 people is increasing by 15% each year. How much will the population be in 5 years?
According to the compound interest formula, the population is 5 years is 422,385.
The term compound interest in math is defined as the interest calculated on the principal and the interest accumulated over the previous period.
Here we have given that the population of 210,000 people is increasing by 15% each year.
And then while looking into the given question, we have identified that the value of
interest rate = 15%
principal count = 210,000
time period = 5
Here we have to convert R as a percent to r as a decimal, then we get
=> r = R/100
=> r = 15/100
=> r = 0.15 rate per year,
Now, we have to solve the equation for A
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
Apply the values on it , then we get,
[tex]A = 210,000.00(1 + \frac{0.15}{1} )^{(1)(5)}[/tex]
When we simplify this one then we get
[tex]A = 210,000.00(1 + 0.15)^5[/tex]
Therefore, the value of A is 422,385.
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How do you find the 3rd side of a triangle?
The third side of a triangle, the following formula can be used c² = a² + b² - 2abcos(C)
To calculate the third side of a triangle, first find the lengths of the other two sides and the angle opposite the third side. Then plug these values into the formula above and solve for c.
Where c is the third side of the triangle, a and b are the other two sides, and C is the angle between them.
For example, for a triangle with two sides of length 4 and 6, and an angle between them of 75 degrees, the formula would look like this:
c² = 42 + 62 - 2(4)(6)cos(75)
Solving for c yields a third side length of 8.4.
To solve for c, first square the two side lengths: 42 = 16 and 62 = 36. Then, multiply the two side lengths together and multiply by the cosine of the angle between them: 2(4)(6)cos(75) = 43.9. Finally, add the two squared values together and subtract the result of the multiplication: 16 + 36 - 43.9 = 8.1. Then, take the square root of this result to get the length of the third side: √8.1 = 8.4.
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23. We are laying new carpet in the classroom which is 84 square feet. If the width is 5 feet
more than the length, what are the dimensions of the floor?/
Let l be the length of the classroom in feet, and w be the width of the classroom in feet. We know that l + 5 = w and l * w = 84.
We can use these two equations to solve for the length and width of the classroom.
First, we can solve the second equation for l:
l = 84 / w
Substituting this expression for l into the first equation gives us:
84 / w + 5 = w
Expanding the left side of the equation gives us:
84 / w + 5 = w
84 / w = w - 5
84 = w^2 - 5w
w^2 - 5w - 84 = 0
This is a quadratic equation that we can solve using the quadratic formula:
w = (5 + sqrt(5^2 - 4 * 1 * -84)) / 2 * 1
= (5 + sqrt(25 + 336)) / 2
= (5 + sqrt(361)) / 2
= (5 + 19) / 2
= 24 / 2
= 12
Now that we know the value of w, we can substitute it back into the equation l = 84 / w to find the value of l:
l = 84 / 12
= 7
Therefore, the dimensions of the classroom are 7 feet by 12 feet.
Determine two numbers that have a
square root between 326 and 327, are
divisible by 100, and are a multiple of 6.
It divides by three. According to the law of divisibility for three, a number is fully divisible by three if its digit sum is likewise divisible by three.
What is divisibility test?The divisibility rule is a clear and useful method for determining if an integer is divisible by a given set of divisors without actually doing division, sometimes simply looking at the integer's digits. The divisibility test allows you to rapidly determine if a given integer can be divided by a specified divisor without actually doing the division process. The quotient must be an integer and the remainder must be zero when dividing two numbers precisely.
here
add all the numbers,
326 = 3+2+6 = 11
so it is not divisible by 3
327 = 3+ 2 + 7 = 12
so it is divisible by 3
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A taxicab company charges $2.30 plus $0.80 per mile. Carmen paid a fare of $11.90. Enter and solve an equation to find the number of miles she traveled. Use m as your variable.
The number of miles the taxicab traveled is 12.
The area of mathematics known as algebra aids in the representation of circumstances or problems into mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division.
Given that,
The fixed charges = $ 2.30
Additional charges per miles = $ 0.80,
Thus, the additional charges for x number of miles = $ 0.80x
So, the total charges for x number of miles = Fixed charges + additional charges
=> 2.30 + 0.80x
According to the question,
2.30 + 0.80x = 11.90 (this is the required equation)
Subtracting 2.30 from both sides,
0.80x = 9.6
Dividing both sides by 0.80
x = 12
Hence, the taxicab traveled 12 miles.
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Type the correct answer in each box. Use numerals instead of words. Find the missing side and angle measures in triangle ABC. Round your answers to the nearest tenth. Scalene triangle ABC with side AC labeled 23 and side BC labeled 15. Angle A measures 40 degrees. The measure of angle B is approximately . The measure of angle C is approximately . The length of side AB is approximately
The measures of the angles of the triangles are
The measure of ∠B = 80.3°
The measure of ∠C = 59.7°
The length of side AB = 20.2 units
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of side AC = 23
The measure of side BC = 15
The measure of ∠A = 40°
From the law of sines , we get
( sin A ) / a = ( sin B ) / b = ( sin C ) / c
Substitute the value of A and a in the equation , we get
sin ( 40 )° / 15 = sin B / 23
On simplifying the equation , we get
sin B = ( 23/15 ) x sin ( 40 )°
Now , m∠B = 80.27°
So , the measure of angle ∠B = 80.3°
And ,
The interior angles of a triangle is 180°
So , The measure of angle ∠C = 180° - ( 80.3° + 40° )
On simplifying the equation , we get
The measure of angle ∠C = 59.7°
Now ,
From the law of cosines , c² = a² + b² - 2ab ( cos C )
Substitute the value of a , b and cos C in the equation , we get
c² = 15² + 23² - 2 ( 15 ) ( 23 ) cos ( 59.7 )°
On simplifying the equation , we get
c² = 225 + 529 - 348.12363
c² = 405.87
Taking square roots on both sides of the equation , we get
c = 20.156
c = 20.2 units
Therefore, the measure of side AB = 20.2 units
Hence , the measures angles of triangle is solved
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How do I find prime factorization?
Answer:
One way is to make a factor tree. She below for examples.
Step-by-step explanation:
Answer:
You basically just count jumps of that number
Given that there are 3 feet or 36 inches in 1 yard, which of the following amounts is greater than 6 feet? Select all that apply. Video A) 2 yards, 3 inches B) 5 feet, 8 inches C) 96 inches D) 3 yards, 2 feet E) 1 yard, 2 feet
Answer: its D
Step-by-step explanation: 3 yard is bigger then 6 feet because 3 yards equals 9 feet hope this helps
Hello good morning do anyone think they could help please
Answer:
1. 15
2. 15
3. 13
4. 11
5. 14
6. 11
7. 18
8. 19
9. 18
10. 14
Step-by-step explanation:
it takes 4 pounds of apples to make 6 cups of apple sauce at this rate how much apple sauce can you make with 10 pounds of apples
Answer: 12 cups of applesauce
Step-by-step explanation:
Write 5 2/3+2 1/5 as a mixed number
Answer: 7 13/15
Step-by-step explanation:
First of, you have to get your common denominator, as it's impossible without one.
The closest common denominator is 15, and it will ask you for a simplified version.
Multiply the 2/3 in 5 2/3 by 5 on both sides to get 5 10/15
Multiply the 1/5 in 2 1/5 by 3 on both sides to get 2 3/15
Then add up your sum.
5 10/15+2 3/15=7 13/15
Answer:
7 13/15
Step-by-step explanation:
5 2/3+2 1/5
We need to get a common denominator for the fraction
3*5 = 15
2/3 *5/5 = 10/15
1/5 * 3/3 = 3/15
5 10/15 + 2 3/15 = 7 13/15
HELP PLEASEEEEEEEEEEEEEEEE
Answer: The answer is $1,317.50
Step-by-step explanation:
First, Find how much they earn in the goods sale.
Make $1,700, their goal to earn, into 1,700/1 and set it to multiply that by 2/5, the fractional amount of money earnt at the goods sale proportional to how much they have to earn.
Simplify that by crossing 1,700 and 5 into a 340 and 1.
Multiply 340/1 by 2/1 to get 680/1.
Make that into a whole number ($680) to show how much money earnt from the goods sale.
Secondly, find how much money they earn by the Bingo Night
Make 1,700, like last time, into 1,700/1 and set it to multiply 3/8, the fractional amount of money earnt from the Bingo Night proportional to how much they have to earn
You can't simplify, so just multiply the amount.
If you multiply, you will get 5,100/8.
Divide 5,100 by 8 (the divisor by the dividend).
Make sure to also add the 0 after the tenths place after you get your quotient, which is supposed to be 637.5 (or $637.50)
Lastly, You have to add them up.
Add $637.50+$680.
You shall get $1,317.50
The diagram shows an isosceles triangle. All the measurements are in cm, work out the perimeter of the triangle.
I need to know how to solve e,d,f im so confused it’s about angles in a circle
When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.
what is circle ?A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric about the center at every angle. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetric about the center at every angle.
given
in 6th figure
61° + 52° + x = 180° ( sum of exterior angle )
113° + x = 180°
x = 67°
y = 67°
When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.
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