Problem 77 - Introductory Algebra for College Students

Question

What are supplementary angles? Describe how to find the measure of an angle's supplement.

Step-by-Step Solution

Answer

Supplementary angles are two angles whose measures add up to 180 degrees. The measure of an angle's supplement can be found by subtracting the given angle from 180 degrees.

Step 1: Understand The Concept of Supplementary Angles

In geometry, when two angles add up, or sum, to 180 degrees, those angles are said to be supplementary angles. In other words, if you have two angles, angle A and angle B, and if the sum of the measures of those angles equals 180 degrees, then those two angles are supplementary. Mathematically, this concept can be expressed as: If Angle A + Angle B = 180 degrees, then Angle A and Angle B are supplementary angles.

Step 2: Finding the Measure of an Angle's Supplement

To find the measure of an angle's supplement, subtract the given angle from 180 degrees. This is because the sum of an angle and its supplementary angle is always 180 degrees. Therefore, if you are given an angle, say angle A, and you need to find its supplement, you subtract the measure of angle A from 180 degrees. Mathematically, this can be expressed as: Supplement of Angle A = 180 degrees − Angle A.

Step 3: Example

For example, if Angle A = 50 degrees, then to find its supplementary angle, subtract 50 degrees from 180 degrees. This gives: Supplement of angle A = 180 - 50 = 130 degrees. Hence, the supplement of Angle A is 130 degrees.