Supplementary - Complementary Angles. online exercise for | Live ... - Free Printable

Problem Analysis:

The worksheet involves three sections related to complementary and supplementary angles. Let's solve each section step by step.

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Section I: Complementary Angles

Complementary angles are two angles whose measures add up to 90°.

#### Given angles:
1. \( 20^\circ \)
2. \( 67^\circ \)
3. \( 14^\circ \)
4. \( 81^\circ \)
5. \( 45^\circ \)

#### Solution:
- For \( 20^\circ \):
\( 90^\circ - 20^\circ = 70^\circ \)

- For \( 67^\circ \):
\( 90^\circ - 67^\circ = 23^\circ \)

- For \( 14^\circ \):
\( 90^\circ - 14^\circ = 76^\circ \)

- For \( 81^\circ \):
\( 90^\circ - 81^\circ = 9^\circ \)

- For \( 45^\circ \):
\( 90^\circ - 45^\circ = 45^\circ \)

#### Answers:
\[
\boxed{70^\circ, 23^\circ, 76^\circ, 9^\circ, 45^\circ}
\]

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Section II: Supplementary Angles

Supplementary angles are two angles whose measures add up to 180°.

#### Given angles:
1. \( 120^\circ \)
2. \( 56^\circ \)
3. \( 29^\circ \)
4. \( 162^\circ \)
5. \( 83^\circ \)

#### Solution:
- For \( 120^\circ \):
\( 180^\circ - 120^\circ = 60^\circ \)

- For \( 56^\circ \):
\( 180^\circ - 56^\circ = 124^\circ \)

- For \( 29^\circ \):
\( 180^\circ - 29^\circ = 151^\circ \)

- For \( 162^\circ \):
\( 180^\circ - 162^\circ = 18^\circ \)

- For \( 83^\circ \):
\( 180^\circ - 83^\circ = 97^\circ \)

#### Answers:
\[
\boxed{60^\circ, 124^\circ, 151^\circ, 18^\circ, 97^\circ}
\]

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Section III: Finding Missing Angle Measures

This section involves determining the missing angle measures in various geometric configurations. We use properties of complementary, supplementary, and adjacent angles, as well as the fact that the sum of angles around a point is 360° and the sum of angles on a straight line is 180°.

#### Diagrams and Solutions:

1. Diagram N:
- Given: \( 60^\circ \) (adjacent to a right angle).
- The missing angle is complementary to \( 60^\circ \):
\( 90^\circ - 60^\circ = 30^\circ \).
- Answer: \( 30^\circ \)

2. Diagram E:
- Given: \( 28^\circ \) (adjacent to a right angle).
- The missing angle is complementary to \( 28^\circ \):
\( 90^\circ - 28^\circ = 62^\circ \).
- Answer: \( 62^\circ \)

3. Diagram T:
- Given: \( 47^\circ \) (adjacent to a right angle).
- The missing angle is complementary to \( 47^\circ \):
\( 90^\circ - 47^\circ = 43^\circ \).
- Answer: \( 43^\circ \)

4. Diagram L:
- Given: \( 72^\circ \) (on a straight line).
- The missing angle is supplementary to \( 72^\circ \):
\( 180^\circ - 72^\circ = 108^\circ \).
- Answer: \( 108^\circ \)

5. Diagram W:
- Given: \( 116^\circ \) (on a straight line).
- The missing angle is supplementary to \( 116^\circ \):
\( 180^\circ - 116^\circ = 64^\circ \).
- Answer: \( 64^\circ \)

6. Diagram F:
- Given: \( 35^\circ \) (on a straight line).
- The missing angle is supplementary to \( 35^\circ \):
\( 180^\circ - 35^\circ = 145^\circ \).
- Answer: \( 145^\circ \)

7. Diagram E:
- Given: \( 34^\circ \) (in a right triangle).
- The missing angle is complementary to \( 34^\circ \):
\( 90^\circ - 34^\circ = 56^\circ \).
- Answer: \( 56^\circ \)

8. Diagram B:
- Given: \( 67^\circ \) (in a triangle with a right angle).
- The missing angle is complementary to \( 67^\circ \):
\( 90^\circ - 67^\circ = 23^\circ \).
- Answer: \( 23^\circ \)

9. Diagram N:
- Given: \( 73^\circ \) (adjacent to a right angle).
- The missing angle is complementary to \( 73^\circ \):
\( 90^\circ - 73^\circ = 17^\circ \).
- Answer: \( 17^\circ \)

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Final Answers for Section III:

\[
\boxed{30^\circ, 62^\circ, 43^\circ, 108^\circ, 64^\circ, 145^\circ, 56^\circ, 23^\circ, 17^\circ}
\]

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Complete Answer Key:

1. Section I: \( 70^\circ, 23^\circ, 76^\circ, 9^\circ, 45^\circ \)
2. Section II: \( 60^\circ, 124^\circ, 151^\circ, 18^\circ, 97^\circ \)
3. Section III: \( 30^\circ, 62^\circ, 43^\circ, 108^\circ, 64^\circ, 145^\circ, 56^\circ, 23^\circ, 17^\circ \)

\[
\boxed{70^\circ, 23^\circ, 76^\circ, 9^\circ, 45^\circ, 60^\circ, 124^\circ, 151^\circ, 18^\circ, 97^\circ, 30^\circ, 62^\circ, 43^\circ, 108^\circ, 64^\circ, 145^\circ, 56^\circ, 23^\circ, 17^\circ}
\]