Question

two angles are supplementary. the larger angle is 48 degrees more than 10 times the smaller angle. find the measure of each angle.

Answer 1

The angles are 12 degrees and 168 degrees.  

Answer 2

Smaller angle = 12° and larger angle = 168°.

Explanation:

It is given that the two angles are supplementary. It means their sum of 180°.

Let x be smaller angle.

The larger angle is 48 degrees more than 10 times the smaller angle.

Larger angle =
`10x+48`

Since both angles are supplementary angles, so

Smaller angle + Larger angle = 180°

`x+(10x+48)=180`

`x+10x+48=180`

Combined line terms.

`11x+48=180`

Subtract 48 from both sides.

`11x=180-48`

`11x=132`

Divide both sides by 11.

`x=12`

The value of x is 12. It means the smaller angle is 12°.

Larger angle =
`10x+48=10(12)+48=120+48=168`

Therefore the larger angle is 168°.