Question

Analyze the diagram below and complete the instructions that follow. Find M

Answer 1

Check the picture below.

notice, the missing interior angle is a linear angle with ∡FEG, therefore, both of them add up to 180°, so the missing interior one is the difference of
[ 180° - (x + 4) ].

also recall that the sum of all interior angles in a triangle add up to 180°.

so, let's add them up then,

$\bf x+2x+~~[180~-~(x+40)]~=~180 \\\\\\ 3x+~~[180-x-40]=180 \implies 3x+140-x=180\implies 2x=40 \\\\\\ x=\cfrac{40}{2}\implies \boxed{x=20} \implies \measuredangle FEG=(x+40)\implies \measuredangle FEG = 20+40$