Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 54°

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Identify the given angle measure, which is 54°.

To find the complement of an angle, subtract the angle from 90°. So, calculate 90° - 54°.

To find the supplement of an angle, subtract the angle from 180°. So, calculate 180° - 54°.

The result from step 2 gives you the measure of the complementary angle.

The result from step 3 gives you the measure of the supplementary angle.

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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. To find the complement of a given angle, you subtract the angle's measure from 90 degrees. For example, if the angle is 54°, its complement would be 90° - 54° = 36°.

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 degrees. For instance, for an angle of 54°, the supplement would be 180° - 54° = 126°.

Angle Measurement

Angle measurement is typically expressed in degrees, where a full rotation is 360 degrees. Understanding how to manipulate these measurements is crucial for solving problems involving complementary and supplementary angles. This foundational knowledge allows students to effectively calculate the required angles based on given measures.

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