The Sum of the Measures of Angle X and Angle Y Is 90


Question: The sum of the measures of angle X and angle Y is 90. If the measure of angle X is 30 less than twice the measure of angle Y, what is the measure of angle X?

Angles are usually measured in degrees and denoted by º (the degree symbol), which is a measure of circularity or rotation.

Answer: The measure of angle x is 70°.

Let's find the measure of angle X.

Explanation:

Given that, the sum of the measures of angle X and angle Y is 90º

x + y = 90°       -----------(1)

Also, the measure of angle X is 30 less than twice the measure of angle Y

x = 2y - 30°

x - 2y = 30°      -----------(2)

So, by solving equation (1) and equation (2), by the method of elimination, we get:

          x + y = 90°

     (-)  x - 2y = 30° 

                3y = 60°

y = 60°/3

y = 20° 

By substitution of value of y in equation (1):

x + y = 90° 

x + 20° = 90° 

x = 90° - 20° 

x = 70° 

Thus, the measure of angle x is 70°.