Question

The measure of the supplement of an angle is three times the measure of the complement of the angle. How do you find the measures of the angles?

Answer 1

Both angles are `45^@`

Explanation:

`m + n = 90`
as an angle and its complement equal 90

`m + 3n = 180`

as an angle and its supplement equals 180

Subtracting both equations will eliminate m

`m + 3n -m - n= 180-90` this gives

`2n = 90` and dividing both sides by `2` gives

`2n/2 = 90/2` so

`n = 45`

substituting `45` for `n` gives

`m + 45 = 90` subtracting `45` from both sides gives.

`m + 45 - 45 = 90 - 45` so

`m = 45`

Both the angle and it complement are `45`

The supplement is `3 xx 45 = 135`