Question

1. these two angles are: supplementary complementary angle x =
2. these two angles are: supplementary complementary angle x =

given: ∠1 = 90° ∠2 = 34° ∠6 = 137°

1. < 3 = 90°
2. < 8 =
3. < 4 =

Explanation:

Step1: Recall angle - relationship definitions

Two angles are supplementary if their sum is 180°. Two angles are complementary if their sum is 90°.

Step2: Solve for angle \(x\) in problem 11

The given angle is 85°. Since the two angles are supplementary, we use the formula \(x + 85^{\circ}=180^{\circ}\). Then \(x = 180^{\circ}-85^{\circ}=95^{\circ}\).

Step3: Solve for angle \(x\) in problem 12

The given angle is 32°. Since the two angles are complementary, we use the formula \(x + 32^{\circ}=90^{\circ}\). Then \(x=90^{\circ}-32^{\circ}=58^{\circ}\).

Step4: Analyze angles in problem 13 - 15

Given \(\angle1 = 90^{\circ}\), and \(\angle1\) and \(\angle3\) are vertical - angles. Vertical angles are equal, so \(\angle3=90^{\circ}\). Given \(\angle6 = 137^{\circ}\), and \(\angle6\) and \(\angle8\) are vertical - angles, so \(\angle8 = 137^{\circ}\). \(\angle2=34^{\circ}\), and \(\angle2\) and \(\angle4\) are vertical - angles, so \(\angle4 = 34^{\circ}\).

Answer:

1. Angle \(x = 95^{\circ}\)
2. Angle \(x = 58^{\circ}\)
3. \(\angle3 = 90^{\circ}\)
4. \(\angle8 = 137^{\circ}\)
5. \(\angle4 = 34^{\circ}\)