Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 89°

Verified step by step guidance

1. Understand the definitions: The complement of an angle is what, when added to the angle, equals 90°. The supplement of an angle is what, when added to the angle, equals 180°.
2. To find the complement of the given angle, subtract the angle from 90°. Use the formula: Complement = 90° - given angle.
3. To find the supplement of the given angle, subtract the angle from 180°. Use the formula: Supplement = 180° - given angle.
4. Apply the formula for the complement: Complement = 90° - 89°.
5. Apply the formula for the supplement: Supplement = 180° - 89°.

Key Concepts

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. To find the complement of a given angle, you subtract the angle's measure from 90. For example, the complement of an angle measuring 89 degrees is 90 - 89 = 1 degree.

Supplementary Angles

Supplementary angles are two angles whose measures sum to 180 degrees. To determine the supplement of a given angle, you subtract the angle's measure from 180. For instance, the supplement of an angle measuring 89 degrees is 180 - 89 = 91 degrees.

Angle Measurement

Angle measurement is the process of determining the size of an angle in degrees. Angles can be classified as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (between 90 and 180 degrees), or straight (exactly 180 degrees). Understanding these classifications helps in identifying complementary and supplementary relationships.