Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 10°

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Identify the given angle measure, which is 10°.

To find the complement of an angle, use the formula: Complement = 90° - given angle.

Substitute the given angle into the formula: Complement = 90° - 10°.

To find the supplement of an angle, use the formula: Supplement = 180° - given angle.

Substitute the given angle into the formula: Supplement = 180° - 10°.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. For any given angle, its complement can be found by subtracting the angle's measure from 90. For example, if the angle is 10 degrees, its complement would be 90 - 10 = 80 degrees.

Supplementary Angles

Supplementary angles are two angles whose measures sum to 180 degrees. To find the supplement of a given angle, subtract the angle's measure from 180. In the case of a 10-degree angle, the supplement would be 180 - 10 = 170 degrees.

Angle Measurement

Angle measurement is typically expressed in degrees, where a full rotation is 360 degrees. Understanding how to measure and classify angles is fundamental in trigonometry, as it allows for the identification of relationships between angles, such as complementary and supplementary angles, which are essential for solving various geometric problems.

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