Answers:
The three interior angles are
Angle M = 73
Angle A = 75
Angle T = 32
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Explanation:
Check out the attached image. This is optional but helpful in my opinion to see how the three interior angles are formed.
The exterior angle of A is 105, so the interior angle of A is 180-105 = 75. Subtract the exterior angle from 180 to get the interior counterpart.
Do the same for angle M: 180-(2x+27) = 180-2x-27 = 153-2x
The interior angle for T is x-8 as the interior angle and the "x-8" angle shown are vertical angles, so they are congruent.
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So far, we found the three interior angles to be
A = 75
M = 153-2x
T = x-8
Add up these three interior angles, set it equal to 180, solve for x
A+M+T = 180
75+153-2x+x-8 = 180
-x+220 = 180
-x+220-220 = 180-220
-x = -40
x = 40
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If x = 40, then...
interior angle M = 153-2x = 153-2*40 = 73
interior angle T = x-8 = 40-8 = 32
As a check, note how the three interior angles add to 180:
A+M+T = 75+73+32 = 180
