Textbook Question
Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 50° 40' 50"
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1. Measuring Angles
Complementary and Supplementary Angles
2:36 minutesProblem 15
Textbook Question
Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 54°
Verified step by step guidance1
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°.
To find the complement of the given angle (54°), set up the equation: \(\text{complement} + 54^\circ = 90^\circ\).
Solve for the complement by subtracting 54° from 90°: \(\text{complement} = 90^\circ - 54^\circ\).
To find the supplement of the given angle (54°), set up the equation: \(\text{supplement} + 54^\circ = 180^\circ\).
Solve for the supplement by subtracting 54° from 180°: \(\text{supplement} = 180^\circ - 54^\circ\).
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Video duration:
2mKey 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, subtract the angle's measure from 90°. For example, the complement of 54° is 90° - 54° = 36°.
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Intro to Complementary & Supplementary Angles
Supplementary Angles
Supplementary angles are two angles whose measures add up to 180 degrees. To find the supplement of a given angle, subtract the angle's measure from 180°. For example, the supplement of 54° is 180° - 54° = 126°.
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Angle Measurement and Units
Angles are measured in degrees, representing the amount of rotation between two rays. Understanding how to manipulate and interpret these measurements is essential for solving problems involving complements and supplements.
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