Question

geometry question 7, 6.1.31 identify the pairs of supplementary angles. choose all that apply. a. ∠tpr and ∠rpt b. ∠spq and ∠qpt c. ∠rps and ∠spr d. ∠qpt and ∠rpt e. ∠spr and ∠rpt f. ∠qpt and ∠tpq g. ∠spr and ∠qpt h. ∠spq and ∠spr

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180°.

Step2: Analyze each option

• Option A: ∠TPR and ∠RPT are the same angle, not a pair of supplementary angles.
• Option B: ∠SPQ = 130° and ∠QPT = 50°, 130°+50° = 180°, so they are supplementary.
• Option C: ∠RPS and ∠SPR are the same angle, not a pair of supplementary angles.
• Option D: ∠QPT = 50° and ∠RPT = 130°, 50°+130° = 180°, so they are supplementary.
• Option E: ∠SPR = 50° and ∠RPT = 130°, 50°+130° = 180°, so they are supplementary.
• Option F: ∠QPT and ∠TPQ are the same angle, not a pair of supplementary angles.
• Option G: ∠SPR = 50° and ∠QPT = 50°, 50°+50°≠180°, so they are not supplementary.
• Option H: ∠SPQ = 130° and ∠SPR = 50°, 130°+50° = 180°, so they are supplementary.

Answer:

B. ∠SPQ and ∠QPT
D. ∠QPT and ∠RPT
E. ∠SPR and ∠RPT
H. ∠SPQ and ∠SPR