Question

Use an algebraic equation to find the measures of two angles described below. Begin by letting x represent the degree measure of the angle's complement. The measure of the angle is 14 degrees greater than its complement What is the measure of the complement and the measure of the other angle.

Answer 1

Angle =
`52^\circ`

Complement angle =
`38^\circ`

Explanation:

We are given the following information:

x is the degree of a an angles complement. Thus, we can write:

`90^\circ - \text{Angle Measure} = x`

We are also given that angle measure is greater than the complement by 14 degree measure.

`\text{Angle Measure} = x + 14`

Putting value of angle measure in first equation, we get:

`90 - ( x + 14 ) = x\\90 -x -14 = x\\76 = 2x\\x = 38`

Hence Complement measure =
`38^\circ`

Angle measure = ( 90-38) =
`52^\circ`