Use the image to answer the question.

Question

An illustration shows five points upper L, upper M, upper N, upper O, and upper P. Five rays from a common vertex at upper Q extend through the five points. The rays extend beyond the five points with an arrow on one side. The rays upper Q upper L, upper Q upper M, upper Q upper N, upper Q upper O, and upper Q upper P join the points from upper Q. The ray upper Q upper M extends horizontal to the left of upper Q. The ray upper Q upper N extends upward to the left of upper Q. The ray upper Q upper O is inclined upward to the right of upper Q. The ray upper Q upper P is horizontal to the right of upper Q. The ray upper Q upper L extends to the bottom left of upper Q. Angle upper N upper Q upper O is marked with a right angle symbol. Angle upper P upper Q upper O is labeled 50 degrees.

What two angles are complementary angles?

(1 point)
Responses

∠LQM
and ∠MQN
angle upper L upper Q upper M and angle upper M upper Q upper N

∠MQN
and ∠NQO
angle upper M upper Q upper N and angle upper N upper Q upper O

∠MQL
and ∠LQP
angle upper M upper Q upper L and angle upper L upper Q upper P

∠LQP
and ∠PQO
angle upper L upper Q upper P and angle upper P upper Q upper O
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Answer 1

To determine which two angles are complementary, we need to recall that complementary angles are two angles whose measures add up to 90 degrees.

From the information provided:

• Angle \( \angle NQO \) is a right angle, which means it measures \( 90 \) degrees.
• Angle \( \angle PQO \) is \( 50 \) degrees.

The only pair of angles that adds up to \( 90 \) degrees among the options provided includes \( \angle PQO \) and \( \angle NQO \):

• Since \( \angle NQO = 90 \) degrees, and we are looking for a pair that totals \( 90 \). The pair of angles \( \angle NQO \) and \( \angle PQO\) does not work, instead we are looking for the one which include others since it doesn’t make sense in their nature to pair the same angle.

However, checking with provided options again:

• \( \angle NQM \) and \( \angle MQO \) are complementary angles which adds until right angle.

Thus, the correct response is: Angle \( \angle MQL \) and angle \( \angle LQP \), as they would represent a complement with respect to \( \angle NQO=90\)degrees.