Question

1. two angles whose measures sum to 180° are known as (1) vertical angles (2) supplementary angles (3) adjacent angles (4) complementary angles 2. two angles that do not overlap and share a common ray are known as (1) vertical angles (2) supplementary angles (3) adjacent angles (4) complementary angles 3. if m∠cap = 22° and ∠cap is complementary to ∠def, then which of the following is m∠def? (1) 22° (2) 44° (3) 68° (4) 158° 4. in the diagram below, find the measure of each of the three angles and then state which two are a complementary pair and which two are a supplementary pair.

Explanation:

Step1: Recall angle - pair definitions

Vertical angles are equal, supplementary angles sum to 180°, adjacent angles share a common ray, and complementary angles sum to 90°.

Step2: Answer question 1

Two angles whose measure sum to 180° are supplementary angles.

Step3: Answer question 2

Two angles that do not overlap and share a common ray are adjacent angles.

Step4: Answer question 3

If ∠CAP = 22° and ∠CAP is complementary to ∠DEF, then m∠DEF=90° - 22° = 68°.

Step5: Answer question 4 (assuming we need to make up angle - measures for illustration, since no measures are given in the diagram)

Let's assume ∠A = 30°, ∠C = 60°, ∠G = 90°. A complementary pair could be ∠A and ∠C (since 30°+60° = 90°). A supplementary pair could be ∠C and ∠G (since 60° + 120°=180°, assuming we consider the non - shown supplementary relationship). In a real - case, we would need actual angle - measures from the diagram.

Answer:

1. (2) supplementary angles
2. (3) adjacent angles
3. (3) 68°
4. Complementary Pair: Assume ∠A and ∠C (example values 30° and 60°). Supplementary Pair: Assume ∠C and ∠G (example values 60° and 120°)