Question

The measure of the supplement of an angle is 20° more than three times the measure of the original angle. What are the measures of the angles?

Answer 1

The original angle is `40^@`.
Its supplement is `140^@`

Explanation:

Recall that the sum of supplemental angles is `180^@`.

Based on the question, an expression can be set up with a variable.

If `x` is the value of the original angle, and `(3x+20)` is equal to its supplement, then
`180=x+(3x+20)`

Solving for x, we get:
`180=4x+20`

`160=4x`

`40=x`

The original angle is `40^@`.

To find the supplement, plug in 40 to the expression that we defined above. The supplement is equal to:
`=3*(40)+20`

`=120 + 20=140`

Its supplement is `140^@`

To check, verify that the two angle measurements meet the definition, meaning they sum to `180^@`

`140^@+40^@=180^@`