Question

n - gen math geometry homework
fluency

1. two angles whose measures sum to 180° are known as

(1) vertical angles
(2) supplementary angles
(3) adjacent angles
(4) complementary angles

1. 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

1. if (mangle cap = 22^{circ}) and (angle cap) is complementary to (angle def), then which of the following is (mangle def)?

(1) (22^{circ})
(2) (44^{circ})
(3) (68^{circ})
(4) (158^{circ})

1. 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 - sum definitions

Complementary angles sum to 90°, supplementary angles sum to 180°, vertical angles are opposite each other when two lines intersect, and adjacent angles share a common ray and a common vertex and do not overlap.

Step2: Solve question 1

Since two angles whose measures sum to 180° are supplementary angles, the answer is (2).

Step3: Solve question 2

Two angles that do not overlap and share a common ray are adjacent angles, so the answer is (3).

Step4: Solve question 3

If ∠CAP is complementary to ∠DEF, and m∠CAP = 22°, then m∠DEF=90° - m∠CAP. So m∠DEF = 90°-22° = 68°, and the answer is (3).

Step5: Solve question 4

Without angle - measure values given in the diagram, we assume based on the provided answers. If ∠A and ∠C are a complementary pair, their sum is 90°. If ∠C and ∠G are a supplementary pair, their sum is 180°.

Answer:

1. (2) supplementary angles
2. (3) adjacent angles
3. (3) 68°
4. Complementary pair: ∠A, ∠C; Supplementary pair: ∠C, ∠G