Question

unit 3 - geometry question 7, 6.1.31 identify the pairs of supplementary angles. choose all that apply. a. ∠rsp and ∠psq b. ∠tsq and ∠qst c. ∠rsp and ∠tsq d. ∠qsp and ∠psq e. ∠tsq and ∠psq f. ∠rst and ∠tsq g. ∠psr and ∠rsp h. ∠rst and ∠rsp

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180°.

Step2: Analyze each pair

• For ∠RSP and ∠PSQ: ∠RSP = 25°, ∠PSQ = 155°, 25°+155° = 180°, so they are supplementary.
• For ∠TSQ and ∠QST: ∠TSQ and ∠QST are the same angle, not a pair of supplementary angles.
• For ∠RSP and ∠TSQ: ∠RSP = 25°, ∠TSQ = 25°, 25°+25°≠180°, not supplementary.
• For ∠QSP and ∠PSQ: ∠QSP and ∠PSQ are the same angle, not a pair of supplementary angles.
• For ∠TSQ and ∠PSQ: ∠TSQ = 25°, ∠PSQ = 155°, 25°+155° = 180°, so they are supplementary.
• For ∠RST and ∠TSQ: ∠RST = 180°, ∠TSQ = 25°, 180°+25°≠180°, not supplementary.
• For ∠PSR and ∠RSP: ∠PSR = 155°, ∠RSP = 25°, 155°+25° = 180°, so they are supplementary.
• For ∠RST and ∠RSP: ∠RST = 180°, ∠RSP = 25°, 180°+25°≠180°, not supplementary.

Answer:

A. ∠RSP and ∠PSQ
E. ∠TSQ and ∠PSQ
G. ∠PSR and ∠RSP