In the diagram, mAngleFLI is 106°, mAngleFLG = (2x – 1)°,
mAngleGLH = (x + 17)°, and mAngleHLI = (4x – 15)°.
Four lines extend from point L. They are lines L F, L G, L H, and L I.
What is the measure of the smallest angle in the diagram?
15°
29°
32°
45°
Answers
Answer:
b. 29°
Step-by-step explanation:
In the given diagram, the smallest angle in the diagram is ∠FLG = 29°.
What is an angle?When to lines are meeting at a point, then the geometrical figure is formed called an angle.
Given, four lines extend from point L.
They are lines LF, LG, LH, and LI.
∠FLI = 106°, ∠FLG = (2x - 1)°, ∠GLH = (x + 17)°, ∠HLI = (4x - 15)°
Here, ∠FLI = ∠FLG + ∠GLH + ∠HLI
106° = (2x - 1)° + (x + 17)° + (4x - 15)°
⇒ (2x - 1)° + (x + 17)° + (4x - 15)° = 106°
⇒ (7x + 1)° = 106°
⇒ 7x = 105
⇒ x = 15
Now, ∠FLG = (2x - 1)° = (2 × 15 - 1)° = 29°
GLH = (x + 17)° = (15 + 17)° = 32°
∠HLI = (4x - 15)° = (4 × 15 - 15)° = 45°
Therefore, the smallest angle in the diagram is ∠FLG = 29°.
Learn more about an angle here:
https://brainly.com/question/14460240
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Answers
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