Question

The sum of the measures of two complementary angles is 90 . If one angle measures 18 more than twice the measure of the other , find the measure of the smaller angle .

Answer 1

24 degrees.

Explanation:

Let's let the two angles be A and B.

First, since they're complementary, they total 90. Thus:

`A+B=90`

If one angle (let's use A) is 18 more than twice the other, this means that:

`A=18+2B`

Substitute this into the first equation:

`18+2B+B=90`

Combine like terms:

`3B+18=90`

Subtract 18 from both sides:

`3B=72`

Divide both sides by 3:

`B=24`

So, angle B is 24 degrees.

And angle A is 2(24)+18=66 degrees.

So, the smaller angle is 24 degrees.

And we're done!