The measure of an angle is 24 more than 4 times its complement. Find the measure of the angle.

Question

I just need the measurement of the angle

Answer 1

Lets call the first angle A and its complement B.

Since they are complements we know:

m∠A+m∠B=90

We also know that

m∠A=4m∠B+24

We can substitute this into the first

4m∠B+24+m∠B=90

Then Solve for m∠B

5m∠B=66

m∠B=66/5

m∠A=4(66/5)+24=(264+120)/5=384/5

Test

384/5+66/5=90

450/5=90

90=90

These Work so the angle is 384/5=76.8