Question

What is the measure of angle 4?

Answer 1

Answer: C) 108 degrees

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Explanation:

Angle 4 is an exterior angle which corresponds to the remote interior angles of 33 degrees and 75 degrees. Through the remote interior angle theorem, we can add the remote interior angles to get the exterior angle

So we simply add 33 and 75 to get 33+75 = 108

If you chose not to use this theorem, then you can find angle three by using the fact that all three angles of the triangle must add to 180 degrees. So,

33+75+(angle 3) = 180
108+(angle 3) = 180
108+(angle 3) - 108 = 180 - 108
angle 3 = 72 degrees

Then use the fact that angle 3 and angle 4 are supplementary

(angle 3) + (angle 4) = 180
72 + (angle 4) = 180
72 + (angle 4) - 72 = 180 - 72
angle 4 = 108 degrees

either way, we get the same answer

Answer 2

∠4 = 75° + 33° = 108°
( Exterior angles )

Answer is C.