Step [tex]1[/tex]
Find the value of x
we know that
m∠FLI=m∠FLG+m∠GLH+m∠HLI ---------> equation [tex]1[/tex]
In this problem we have
m∠FLI=[tex]106[/tex]°
m∠FLG=[tex](2x-1)[/tex]°
m∠GLH=[tex](x+17)[/tex]°
m∠HLI=[tex](4x-15)[/tex]°
Substitute the values in the equation [tex]1[/tex]
[tex]106=(2x-1)+(x+17)+(4x-15)[/tex]
Combine like terms
[tex]106=(2x+x+4x)+(-1+17-15)[/tex]
[tex]106=(7x)+(1)[/tex]
[tex]7x=105[/tex]
[tex]x=15[/tex]°
Step [tex]2[/tex]
Find the value of each angle
Substitute the value of x in each angle
m∠FLG=[tex](2*15-1)=29[/tex]°
m∠GLH=[tex](15+17)=32[/tex]°
m∠HLI=[tex](4*15-15)=45[/tex]°
therefore
the answer is
The smallest angle in the diagram is [tex]29\ degrees[/tex]
