Multiple Choice
Which type of angle has a measure greater than and less than ?
79
views
1. Measuring Angles
Complementary and Supplementary Angles
4:59 minutesProblem 22
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"
Verified step by step guidance1
Understand the definitions: The complement of an angle is what, when added to the angle, equals 90 degrees, and the supplement of an angle is what, when added to the angle, equals 180 degrees.
Convert the given angle 50° 40' 50" into a consistent format if needed, but since the problem is in degrees, minutes, and seconds, we can work directly with these units.
To find the complement, subtract the given angle from 90° 0' 0" using the subtraction of degrees, minutes, and seconds carefully:
\[ \text{Complement} = 90^\circ 0' 0'' - 50^\circ 40' 50'' \]
To find the supplement, subtract the given angle from 180° 0' 0" similarly:
\[ \text{Supplement} = 180^\circ 0' 0'' - 50^\circ 40' 50'' \]
Perform the subtraction step-by-step, borrowing minutes and seconds as necessary to handle the subtraction of minutes and seconds correctly.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
4mKey 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°. This concept is essential for problems involving right angles and angle pairs.
Recommended video:
3:35
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°. This concept is important when dealing with straight lines and linear pairs of angles.
Recommended video:
3:35Intro to Complementary & Supplementary Angles
Angle Measurement in Degrees, Minutes, and Seconds
Angles can be measured in degrees (°), minutes ('), and seconds ("). One degree equals 60 minutes, and one minute equals 60 seconds. Properly converting and subtracting these units is crucial when calculating complements and supplements of angles given in this format.
Recommended video:
5:31Reference Angles on the Unit Circle
Related Videos
Related Practice