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"

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 degrees. In this case, for an angle of 50° 40' 50", you would convert the angle into a single unit (degrees) and then perform the subtraction to find the complement.

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 the angle of 50° 40' 50", you will similarly convert it to a single unit and subtract it from 180 degrees to find the supplement.

Angle Measurement Units

Angles can be measured in degrees, minutes, and seconds, where 1 degree equals 60 minutes and 1 minute equals 60 seconds. When performing calculations involving angles, it is essential to ensure that all measurements are in the same unit. For example, converting 50° 40' 50" into decimal degrees may simplify the process of finding both the complement and supplement.