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Question

Complementary Angles Quick Check
1 of 51 of 5 Items
Question
Use the image to answer the 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

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

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

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

∠LQM
and ∠MQN

Answer 1

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

Given:

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

Since complementary angles sum to 90 degrees, we can use \( \angle PQO \) and \( \angle NQO \):

• \( \angle PQO + \angle NQO = 50^\circ + 40^\circ = 90^\circ \).

This information implies that \( \angle NQO \) and \( \angle PQO \) are complementary.

The correct response would thus be:

∠PQU and ∠NQO (angle upper P upper Q upper O and angle upper N upper Q upper O).

However, since this is not an option provided, let's review the choices:

• ∠MQN and ∠NQO (not sufficient information to confirm),
• ∠LQP and ∠PQO (also not directly related to 90 degrees),
• ∠MQL and ∠LQP (not sufficient information),
• ∠LQM and ∠MQN (not related).

Clarification could further allow selection among \( \angle NQO \) and \( \angle PQO \). Therefore I recommend selecting \( \angle NQO \) under the respect of the available options that best approach the complementary definition amid deductions!