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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

∠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

1 answer

To find the complementary angles among the options given, we need to identify pairs of angles that add up to 90 degrees.

From the information provided:

  • We know that angle ∠NQO is a right angle, which means it measures 90 degrees.
  • We also know that angle ∠PQO measures 50 degrees.

To find complementary angles, we look for angles that, when added together, equal 90 degrees:

  1. ∠MQN and ∠NQO - No, this does not apply since NQO is already 90 degrees.
  2. ∠LQP and ∠PQO - We don't have enough information about ∠LQP to determine if these are complementary since ∠PQO is known (50 degrees).
  3. ∠LQM and ∠MQN - We don't know the measures of these angles.
  4. ∠MQL and ∠LQP - Similar to above, we do not know these angle measures to determine if they are complementary.

However, the combination of ∠PQO (which is 50 degrees) and the remaining part of angle ∠NQO (which we know is 90 degrees) would mean we can find the measure of ∠LQP (which must be 40 degrees) to satisfy the 90 degrees requirement with ∠PQO.

Thus, the complementary angle pair can logically be:

∠LQP and ∠PQO since:

  • 40 degrees (LQP) + 50 degrees (PQO) = 90 degrees.

Considering all information, the answer is:

∠LQP and ∠PQO.