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°

Question

contestada

Respuesta :

erikayb04 erikayb04 · Answer 1 · 2020-12-15T17:10:46+01:00

Answer:

b. 29°

Step-by-step explanation:

Answer Link

RajarshiG RajarshiG · Answer 2 · 2022-06-15T21:14:09+02:00

In the given diagram, the smallest angle in the diagram is ∠FLG = 29°.

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

#SPJ2