Question

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

Answer 1

Answer:

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

Step-by-step 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 $m\angle FLI$

Answer 2

Answer:

B)29

Step-by-step explanation:

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