Question

1. if two angles add up to 180° they are ______________ angles.
2. if two angles add up to 90°, they are ______________ angles.

one angle of a pair of complementary angles is given. what is the measurement of the other angle?

1. 45° ____ 4. 82° __ 5. 23° ____

one angle of a pair of supplementary angles is given. what is the measurement of the other angle?

1. 173° ____ 7. 75° __ 8. 92° ____
2. name two pairs of supplementary angles in the figure below.
3. these two angles are: supplementary ____ complementary __ angle x = ____

Explanation:

Step1: Recall angle - sum definitions

If two angles add up to 180°, they are supplementary angles. If two angles add up to 90°, they are complementary angles.

Step2: Find complementary angles

For complementary angles, if one angle is \(a\), the other is \(90 - a\).

• For \(a = 45^{\circ}\), the other angle is \(90^{\circ}-45^{\circ}=45^{\circ}\).
• For \(a = 82^{\circ}\), the other angle is \(90^{\circ}-82^{\circ}=8^{\circ}\).
• For \(a = 23^{\circ}\), the other angle is \(90^{\circ}-23^{\circ}=67^{\circ}\).

Step3: Find supplementary angles

For supplementary angles, if one angle is \(b\), the other is \(180 - b\).

• For \(b = 173^{\circ}\), the other angle is \(180^{\circ}-173^{\circ}=7^{\circ}\).
• For \(b = 75^{\circ}\), the other angle is \(180^{\circ}-75^{\circ}=105^{\circ}\).
• For \(b = 92^{\circ}\), the other angle is \(180^{\circ}-92^{\circ}=88^{\circ}\).

Step4: Identify supplementary - angle pairs in a figure

In the figure with intersecting lines at point \(E\), \(\angle AEB\) and \(\angle BEC\) are supplementary (since they form a straight - line \(\angle AEC\) which is 180°), and \(\angle AED\) and \(\angle DEC\) are supplementary (since they form a straight - line \(\angle ADC\) which is 180°).

Step5: Classify and find angle in the last figure

The two angles in the last figure are supplementary because they form a straight - line. If one angle is \(70^{\circ}\), then \(x=180^{\circ}-70^{\circ}=110^{\circ}\).

Answer:

1. Supplementary
2. Complementary
3. \(45^{\circ}\)
4. \(8^{\circ}\)
5. \(67^{\circ}\)
6. \(7^{\circ}\)
7. \(105^{\circ}\)
8. \(88^{\circ}\)
9. \(\angle AEB\) and \(\angle BEC\), \(\angle AED\) and \(\angle DEC\)
10. Supplementary, \(110^{\circ}\)