Question

ii. name the complementary angles to each of the following: (7.) 45° (8.) 70° (9.) 12° (10.) 62° (11.) 25° (12.) 50°
iii. name the supplementary angle to each of the following: (13.) 120° (14.) 40° (15.) 110° (16.) 25° (17.) 127° (18.) 100°
iv. what angle is complementary to 80°? (a) 10° (b) 80° (c) 170° (d) 180°
(20.) which of the following pairs of angles are supplementary? (a) 45° and 30° (b) 30° and 60° (c) 60° and 60° (d)90° and 90°
(21.) look at the figure below. it shows a number of different angles. which named pair of angles are supplementary to each other? (a) ∠aob and ∠ boc (b) ∠aob and ∠ doe (c) ∠aoc and ∠cod (d) ∠aod and ∠doe

Explanation:

Step1: Recall complementary - angle definition

Complementary angles add up to 90°.

Step2: Find complementary angles for II

(7.) 90° - 45° = 45°
(8.) 90° - 70° = 20°
(9.) 90° - 12° = 78°
(10.) 90° - 62° = 28°
(11.) 90° - 25° = 65°
(12.) 90° - 50° = 40°

Step3: Recall supplementary - angle definition

Supplementary angles add up to 180°.

Step4: Find supplementary angles for III

(13.) 180° - 120° = 60°
(14.) 180° - 40° = 140°
(15.) 180° - 110° = 70°
(16.) 180° - 25° = 155°
(17.) 180° - 127° = 53°
(18.) 180° - 100° = 80°

Step5: Solve IV

For an angle 80°, its complementary angle is 90° - 80° = 10°. So the answer is (a).

Step6: Solve (20.)

Check each pair:
(a) 45°+30°=75°≠180°
(b) 30° + 60°=90°≠180°
(c) 60°+60° = 120°≠180°
(d) 90°+90° = 180°. So the answer is (d).

Step7: Solve (21.)

Supplementary angles add up to 180°. ∠AOD and ∠DOE form a straight - line at O, so ∠AOD+∠DOE = 180°. The answer is (d).

Answer:

II. (7.) 45°; (8.) 20°; (9.) 78°; (10.) 28°; (11.) 65°; (12.) 40°
III. (13.) 60°; (14.) 140°; (15.) 70°; (16.) 155°; (17.) 53°; (18.) 80°
IV. (a) 10°
(20.) (d) 90° and 90°
(21.) (d) ∠AOD and ∠DOE