Question

Supplementary angles differ by 48°. What are the angle's measurements?

Answer 1

The two angles measure 66 degrees and 114 degrees because the sum of supplementary angles is 180 degrees.

Explanation:

Supplementary angles are two angles with a sum of 180 degrees.

Let the smaller angle = `x`

If the two angles differ by 48 degrees, the bigger angle is 48 degrees more and equals `x+48`.

The sum of the two angles is 180, so...

`x + x+48 = 180`

Add the variableterms
`2x +48=180`

Subtract 48 from both sides
`2x=132`

Divide both sides by 2
`(2x)/2 = 132/2`

`x=66` This is the measure of the smaller angle.

The bigger angle = `x+48= 114`