What is the sum of the measures of two complementary angles is 90 If one angle measure is 24 more than twice the measure of the other find the smaller angle?

Answer 1

Angle A = X degrees

Angle B = 2X + 24

A+B = 3X + 24

But

A+B = 90, so

90 = 3x + 24

90 - 24 = 3x

66 = 3x

22 = x

So, Angle A = 22º and Angle B = 22+22+24 = 68º

Here's how to get that answer:

if 2 angles equal 90 degrees, and one angle is 24 more than twice the measure of the other angle, set up an equation with a variable.

Say x is the variable. One angle is 2x+24 because it's twice what x is plus 24. The other angle is x.

2x+24+x+90

Now solve.

Combine the x's to make the equation 3x+24=90.

Now subtract 24 from 90 to get 66.

3x=66

Now divide 66 by 3.

x=22.

We now have to find the measures of both angles.

2x=44, and 44+24=68

the smaller angle is 22 degrees and the bigger angle is 68 degrees.

We know this is right because 22+68=90.