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

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

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

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

∠MQN
and ∠NQO

Answer 1

To determine which two angles are complementary, we need to identify pairs of angles that add up to 90 degrees.

From the provided information:

• ∠NQO is marked with a right angle, meaning it measures 90 degrees.
• ∠PQO is labeled as 50 degrees.

Since complementary angles add up to 90 degrees:

• We can check if ∠PQO (50 degrees) and ∠NQO (90 degrees) are complementary, but since it is already 90, we look for angles involving ∠PQO.

Now, we check the angles mentioned in the options:

• ∠LQP
• ∠PQO (50 degrees)

If we assume ∠LQP is the remaining angle in the situation, it must be such that it complements ∠PQO to make a total of 90 degrees.

Since we have: ∠PQO = 50 degrees, and therefore for complementary angles: ∠LQP + 50 degrees = 90 degrees Thus, ∠LQP must be 40 degrees.

Therefore, the answer is: ∠LQP and ∠PQO (angle upper L upper Q upper P and angle upper P upper Q upper O).

These two angles are complementary since they add up to 90 degrees.