I need help with the following problem:
Directions: Express each answer in simplest form in terms of the given variable.
Problem: An angle has measure Xº. Find the average of the measures of a complement and a supplement of the angle.
To find the average of the measures of a complement and a supplement of an angle, we first need to understand what a complement and a supplement of an angle are.
1. Complement of an angle: The complement of an angle is another angle that, when added to the given angle, will result in a sum of 90 degrees (a right angle).
2. Supplement of an angle: The supplement of an angle is another angle that, when added to the given angle, will result in a sum of 180 degrees (a straight angle).
Now, let's solve the problem.
Given: An angle with measure X degrees.
To find the complement of the angle, we subtract the measure of the angle from 90 degrees (since the sum of an angle and its complement is 90 degrees):
Complement = 90 - X degrees.
To find the supplement of the angle, we subtract the measure of the angle from 180 degrees (since the sum of an angle and its supplement is 180 degrees):
Supplement = 180 - X degrees.
To find the average of the measures of the complement and the supplement, we add the measures of the complement and the supplement and divide the sum by 2:
Average = (Complement + Supplement) / 2
Average = (90 - X + 180 - X) / 2
Average = (270 - 2X) / 2
Average = 135 - X degrees.
Therefore, the average of the measures of the complement and supplement of the angle is 135 degrees minus the measure of the angle (X degrees).