Question

`/_X` and `/_Y` are supplementary. One angle measures 5 times the other angle. What is the complement of the smaller angle?

Answer 1

The complement of the smaller angle measures 60°.

Explanation:

The measures of supplementary angles add up to 180°. So if the angles measure `\theta` and `5\theta`, then

`\theta+5\theta=180°`

`6\theta=180°`

`\theta=30°`

Now we need the complement of this angle. The measures of complementary angles add up to 90°, so:

`90°-\theta=60°`

Answer 2

The smaller angle is `30°` and its complement is `60°`

Explanation:

Let the smaller angle, `hatX,` be `x°`, then the larger angle `hatY` is `5x°`

Supplementary angles add up to `180°`

`x° +5x° = 180°`

`6x° = 180°`

`x = (180°)/6 =30°`

So the smaller angle, `hatX = 30°`

Complementary angles add up to `90°`

So the complement of the smaller angle is `90°-30° = 60°`