Question

Two angles are supplementary. The larger angle measures 120 degrees more than the smaller. What is the degree measure of each angle?

Answer 1

The first angle is 30 degrees. The second angle is 150 degrees. Here's why:

Explanation:

The first angle will be expressed as `x`. Since the second angle is `120` degrees greater than the first, it will be expressed as `(x + 120)`. Because they're supplementary, they'll add up to `180`:

`x + (x + 120) = 180`

Combine like terms.

`2x + 120 = 180`

Subtract 120 from both sides.

`2x = 60`

Divide by 2 to isolate for `x`.

`x = 30`

Plug your data back in:

30 + (30 + 120) = 180

First angle: 30 degrees
Second angle: 150 degrees