Analyze the diagram below and complete the instructions that follow. Find M
1 answer:
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](https://tex.z-dn.net/?f=%5Cbf%20x%2B2x%2B~~%5B180~-~%28x%2B40%29%5D~%3D~180%0A%5C%5C%5C%5C%5C%5C%0A3x%2B~~%5B180-x-40%5D%3D180%0A%5Cimplies%20%0A3x%2B140-x%3D180%5Cimplies%202x%3D40%0A%5C%5C%5C%5C%5C%5C%0Ax%3D%5Ccfrac%7B40%7D%7B2%7D%5Cimplies%20%5Cboxed%7Bx%3D20%7D%0A%5Cimplies%20%0A%5Cmeasuredangle%20FEG%3D%28x%2B40%29%5Cimplies%20%5Cmeasuredangle%20FEG%20%3D%2020%2B40)
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,
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