The angles are complementary angles. Find the measure of each angle.
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A) 40° and 50°
B) 20° and 25°
C) 45° and 45°
D) 80° and 100°

Question

The angles are complementary angles. Find the measure of each angle.
-
A) 40° and 50° 
B) 20° and 25° 
C) 45° and 45° 
D) 80° and 100°

Quizplus · Accepted Answer

Complementary angles add up to 90 degrees. Therefore, we need to solve the system of equations:
x + y = 90 (where x and y are the measures of the two angles)
From the answer choices, we can see that option C is not possible because both angles must be equal to each other. Option D is also not possible because the measure of one angle would have to be greater than 90 degrees. Option B is also not possible because the angles would be too small. Therefore, we are left with option A. Solving for x and y:
x + y = 90
x + 40 = 90 (taking y as 40 degrees)
x = 50
Therefore, the two angles are 50 degrees and 40 degrees, which add up to 90 degrees. Complementary angles add up to 90°. Therefore, the two angles in question must add up to 90°. The only choice that has two angles adding up to 90° is A) 40° and 50°.

The Angles Are Complementary Angles