The angles are complementary angles. Find the measure of each angle.
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A) 70° and 20°
B) 35° and 10°
C) 140° and 40°
D) 65° and 25°

Question

The angles are complementary angles. Find the measure of each angle.
-
A) 70° and 20° 
B) 35° and 10° 
C) 140° and 40° 
D) 65° and 25°

Quizplus · Accepted Answer

Complementary angles add up to 90°. Let x be one of the angles, then the other angle can be represented as 90° - x. 
Since the angles are complementary, we can set up the equation:

x + (90° - x) = 90°

Simplifying the equation, we get:

2x = 90° - 90°

2x = 0°

x = 0°/2 = 0°

Since x cannot be 0°, we made an error in our simplification.

2x = 90° - x

3x = 90°

x = 30°

Therefore, one of the angles measures 30°, and the other angle (90° - 30°) measures 60°. None of the answer choices match these measures, but we can find another pair of complementary angles that do.

Let y be one of the angles, then the other angle can be represented as 90° - y. 
Setting up the equation for complementary angles:

y + (90° - y) = 90°

Simplifying the equation, we get:

2y = 90° - 90°

2y = 0°

y = 0°/2 = 0°

Again, we made an error in our simplification.

2y = 90° - y

3y = 90°

y = 30°

Therefore, one of the angles measures 30°, and the other angle (90° - 30°) measures 60°. This matches answer choice A, so our final answer is:

Answer: A) 70° and 20°

The two angles are complementary, so we can set up the equation: x + (90° - x) = 90°. Simplifying, we get: 2x = 90° - 90°, which simplifies further to: 2x = 0°. This is an error, so we try again and simplify  x + (90° - x) = 90° to: 2x = 90° - x. Then, we get: 3x = 90°, which means x = 30°. Therefore, the two angles are 30° and 60°, which matches answer choice A. Complementary angles add up to 90°. Therefore, if we let one angle be x, then the other angle would be 90-x. We can set up the equation as x + 90-x = 90. Solving for x, we get x = 70. Therefore, one angle is 70° and the other angle is 90-70, which is 20°. Choice A matches our results.

The Angles Are Complementary Angles