Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 14° 20'

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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°.

Convert the given angle 14° 20' into a decimal or keep it in degrees and minutes format for calculation. Remember that 1 degree = 60 minutes.

To find the complement, set up the equation: Complement + 14° 20' = 90°. Rearrange to find Complement = 90° - 14° 20'.

To find the supplement, set up the equation: Supplement + 14° 20' = 180°. Rearrange to find Supplement = 180° - 14° 20'.

Perform the subtraction carefully, handling the minutes properly (if minutes in the angle are greater than the minutes in 90° or 180°, borrow 1 degree = 60 minutes) to find the exact measures of the complement and supplement.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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°. This concept is essential for problems involving right angles and angle pairs.

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°. This concept is important when dealing with straight lines and linear pairs of angles.

Angle Measurement in Degrees and Minutes

Angles can be measured in degrees (°) and minutes ('). One degree equals 60 minutes. When performing calculations, convert minutes properly and carry over values when minutes exceed 60, ensuring accurate results in angle arithmetic.