Question

4. An angle is 50° more than its supplement. Find the angles.
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Answer 1

The angles measure
`65`° and
`115`°.

Explanation:

Supplementary angles are a pair of angles whose measures add up to
`180`°. In this case, we know that one angle is
`50`° bigger than the other one, so if we let the measure of one angle be
`x`, then the measure of the other angle will be
`x+50`. Therefore, we can write the following equation to solve for

`x+x+50=180`

Solving for
`x`, we get:

`x+x+50=180`

`2x+50=180` (Simplify LHS)

`2x+50-50=180-50` (Subtract
`50` from both sides of the equation to isolate
`x`)

`2x=130` (Simplify)

`(2x)/(2)=(130)/(2)` (Divide both sides of the equation by
`2` to get rid of
`x`'s coefficient)

`x=65`

Therefore,
`x+50=65+50=115`, so our final answer is that the angles measure
`65`° and
`115`°. Hope this helps!