Question

determine whether each statement can be assumed from the figure. explain. 9. ∠nqo and ∠oqp are complementary. 10. ∠srq and ∠qrp is a linear pair. 11. ∠mqn and ∠mqr are vertical angles.

Explanation:

Step1: Recall complementary - angles definition

Two angles are complementary if their sum is 90°. From the figure, there is no indication that ∠NQO+∠OQP = 90°. So, we cannot assume ∠NQO and ∠OQP are complementary.

Step2: Recall linear - pair definition

A linear pair of angles are adjacent angles whose non - common sides are opposite rays. In the figure, point R is not on the line formed by S and Q in a way that ∠SRQ and ∠QRP are adjacent with non - common sides as opposite rays. So, we cannot assume ∠SRQ and ∠QRP is a linear pair.

Step3: Recall vertical - angles definition

Vertical angles are two non - adjacent angles formed by two intersecting lines. In the figure, ∠MQN and ∠MQR share a common side MQ, so they are not non - adjacent. So, we cannot assume ∠MQN and ∠MQR are vertical angles.

Answer:

1. No. There is no indication that the sum of ∠NQO and ∠OQP is 90°.
2. No. ∠SRQ and ∠QRP do not form a linear - pair as per the definition.
3. No. ∠MQN and ∠MQR are not non - adjacent as required for vertical angles.