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

Question

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

Quizplus · Accepted Answer

Supplementary angles add up to 180 degrees, so we can solve this problem with the equation: x + y = 180, where x and y are the measures of the angles. To check which choice is correct, we can solve for x and y in each option and see if they add up to 180.

A) 54 + 36 = 90, not 180
B) 103 + 77 = 180, so this is a possible answer
C) 216 + 144 = 360, not 180
D) 108 + 72 = 180, so this is also a possible answer.

Thus, the best choice is D because it is the only option where the measures of the angles add up to 180. Supplementary angles add up to 180°. Therefore, if x and y are the measures of the angles, we have:

x + y = 180

We can solve for either angle by subtracting one of the variables from both sides:

x = 180 - y

Now we can substitute this expression into the first equation:

x + y = 180
(180 - y) + y = 180
180 = 180

This is true for any values of x and y that add up to 180. Therefore, we can choose any answer choice where the sum of the angles is 180.

In choice D, we have 108° and 72°. These angles add up to 180°, so they are supplementary angles. Therefore, choice D is the correct answer.

The Angles Are Supplementary Angles