The angles are supplementary angles. Find the measure of each angle.
-
A) 108° and 72°
B) 103° and 77°
C) 54° and 36°
D) 216° and 144°

Question

The angles are supplementary angles. Find the measure of each angle.
-
A) 108° and 72° 
B) 103° and 77° 
C) 54° and 36° 
D) 216° and 144°

Quizplus · Accepted Answer

Supplementary angles are two angles that add up to 180 degrees. So if one angle is x degrees, the other angle will be 180-x degrees.

Let x be the measure of one of the angles. Then the other angle will be 180-x.

We are given that these angles are supplementary, so we can set up the equation:

x + 180-x = 180

Simplifying and solving for x, we get:

x = 72

So one of the angles is 72 degrees. The other angle is:

180-x = 180-72 = 108

Therefore, the measures of the angles are 72 degrees and 108 degrees, which corresponds to choice A). Supplementary angles add up to 180°. Therefore, if we let x be one of the angles, we have:

x + y = 180

Solving for y, we get:

y = 180 - x

So the measures of the angles are x and 180-x. If we substitute x=72 into these expressions, we get:

x = 72°
180-x = 108°

Therefore, the angles are 72° and 108°, which match Choice A.

The Angles Are Supplementary Angles