Question

In the diagram, mFLI is 106°, mFLG = (2x – 1)°, mGLH = (x + 17)°, and mHLI = (4x – 15)°.

Answer 1

Step $1$

Find the value of x

we know that

m∠FLI=m∠FLG+m∠GLH+m∠HLI ---------> equation $1$

In this problem we have

m∠FLI=$106$°

m∠FLG=$(2x-1)$°

m∠GLH=$(x+17)$°

m∠HLI=$(4x-15)$°

Substitute the values in the equation $1$

$106=(2x-1)+(x+17)+(4x-15)$

Combine like terms

$106=(2x+x+4x)+(-1+17-15)$

$106=(7x)+(1)$

$7x=105$

$x=15$°

Step $2$

Find the value of each angle

Substitute the value of x in each angle

m∠FLG=$(2*15-1)=29$°

m∠GLH=$(15+17)=32$°

m∠HLI=$(4*15-15)=45$°

therefore

the answer is

The smallest angle in the diagram is $29\ degrees$

Answer 2

The second one and it = 29