Question

1. these two angles are: supplementary __ complementary angle x = 12. these two angles are: supplementary complementary angle x = given: ∠1 = 90° ∠2 = 34° ∠6 = 137° 13. < 3 = ° 14. < 8 = ° 15. < 4 = __ °

Explanation:

Step1: Recall angle - relationship definitions

Supplementary angles add up to 180°, and complementary angles add up to 90°.

Step2: Solve for question 11

The two angles 85° and x are on a straight - line. Since the sum of angles on a straight - line is 180°, they are supplementary.
We use the equation 85°+x = 180°. Solving for x gives x=180° - 85°=95°.

Step3: Solve for question 12

The two angles 32° and x are part of a right - angle (90°). Since the sum of these two angles is 90°, they are complementary.
We use the equation 32°+x = 90°. Solving for x gives x = 90°-32° = 58°.

Step4: Solve for question 13

∠1 = 90° and ∠1 and ∠3 are vertical angles. Vertical angles are equal. So ∠3=90°.

Step5: Solve for question 14

∠6 = 137° and ∠8 and ∠6 are vertical angles. Vertical angles are equal. So ∠8 = 137°.

Step6: Solve for question 15

∠2 = 34° and ∠4 and ∠2 are vertical angles. Vertical angles are equal. So ∠4=34°.

Answer:

1. Supplementary; 95°
2. Complementary; 58°
3. 90
4. 137
5. 34