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

Answer:

24 degrees.

Step-by-step 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!