Answer:
The measure of the smallest angle is [tex]m\angle FLI=29^o[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
we know that
[tex]m\angle FLI=m\angle\ FLG+m\angle GLH+m\angle HLI[/tex] ---> by Angle Addition Postulate
substitute the given values
[tex]106^o=(2x-1)^o+(x+17)^o+(4x-15)^o[/tex]
solve for x
[tex]106^o=(7x+1)^o[/tex]
[tex]7x=106-1\\7x=105\\x=15[/tex]
Find the measure of each angle
substitute the value of x
[tex]m\angle FLI=(2(15)-1)=29^o\\m\angle GLH=(15+17)=32^o\\m\angle HLI=(4(15)-15)=45^o[/tex]
therefore
The measure of the smallest angle is [tex]m\angle FLI[/tex]
