A figure consists of five angle measures: 17°, 34°, 90°, 120°, and 73°. Which two angles measures correspond to complementary angles?
Responses
120° and 17°
120° and 90°
17° and 73°
73° and 34°
The two angle measures that correspond to complementary angles in this figure are 90° and 17°.
explain
Complementary angles are pairs of angles that, when added together, result in a sum of 90°. In the given figure, the angle measures are 17°, 34°, 90°, 120°, and 73°.
We can find the pairs of angles that add up to 90° by adding the angles together:
17° + 34° = 51°
17° + 90° = 107°
17° + 120° = 137°
17° + 73° = 90°
Out of these pairs, only 17° + 73° = 90°. Therefore, the angles 17° and 73° are complementary angles in the given figure.
A right angle consists of two adjacent complementary angles. If one angle measure is 35°, what is the other angle measure?
Responses
55°
125°
65°
145°
Explain
If one angle in a right angle measures 35°, then the other angle in the right angle must be its complementary angle. Complementary angles add up to 90°.
To find the complementary angle, we subtract the given angle measure from 90°:
90° - 35° = 55°
Therefore, the other angle measure in the right angle is 55°.
A figure displays two complementary nonadjacent angles. If one angle measure is 79°, what is the other angle measure?
Responses
101°
121°
11°
21°
explain
Complementary angles add up to 90°. In the given figure, one angle measure is 79°, and we need to find the measure of the other complementary angle.
To find the other angle measure, we subtract the given angle measure from 90°:
90° - 79° = 11°
Therefore, the other angle measure in the figure is 11°.