Question

What is the measure of the smallest angle in the diagram?

In the diagram, mZFLI is 106°, m ZFLG = (2x - 1)",
mZGLH = (x + 17), and m ZHLI = (4x – 15).
15
29°

Answer 1

B)29

Explanation:

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Answer 2

The measure of the smallest angle is
`m\angle FLI=29^o`

Explanation:

The picture of the question in the attached figure

we know that

`m\angle FLI=m\angle\ FLG+m\angle GLH+m\angle HLI` ---> by Angle Addition Postulate

substitute the given values

`106^o=(2x-1)^o+(x+17)^o+(4x-15)^o`

solve for x

`106^o=(7x+1)^o`

`7x=106-1\\7x=105\\x=15`

Find the measure of each angle

substitute the value of x

`m\angle FLI=(2(15)-1)=29^o\\m\angle GLH=(15+17)=32^o\\m\angle HLI=(4(15)-15)=45^o`

therefore

The measure of the smallest angle is
`m\angle FLI`