Question

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 option

• Option A: $\angle RSP = 155^{\circ}$, $\angle PSQ=25^{\circ}$, $\angle RSP+\angle PSQ = 155^{\circ}+25^{\circ}=180^{\circ}$.
• Option B: $\angle TSQ$ and $\angle QST$ are the same angle, not a pair of supplementary angles.
• Option C: $\angle RSP = 155^{\circ}$, $\angle TSQ = 155^{\circ}$, $\angle RSP+\angle TSQ=155^{\circ}+155^{\circ}=310^{\circ}

eq180^{\circ}$.

• Option D: $\angle QSP = 25^{\circ}$, $\angle PSQ = 25^{\circ}$, $\angle QSP+\angle PSQ=25^{\circ}+25^{\circ}=50^{\circ}

eq180^{\circ}$.

• Option E: $\angle TSQ = 155^{\circ}$, $\angle PSQ = 25^{\circ}$, $\angle TSQ+\angle PSQ=155^{\circ}+25^{\circ}=180^{\circ}$.
• Option F: $\angle RST$ is a full - circle angle (360°) not relevant here, and $\angle TSQ = 155^{\circ}$, $\angle RST+\angle TSQ

eq180^{\circ}$.

• Option G: $\angle PSR = 25^{\circ}$, $\angle RSP = 155^{\circ}$, $\angle PSR+\angle RSP=25^{\circ}+155^{\circ}=180^{\circ}$.
• Option H: $\angle RST$ (360°) and $\angle RSP = 155^{\circ}$, $\angle RST+\angle RSP

eq180^{\circ}$.

Answer:

A. $\angle RSP$ and $\angle PSQ$, E. $\angle TSQ$ and $\angle PSQ$, G. $\angle PSR$ and $\angle RSP$