Question

What are the measures of angle A and angle B when angle A is

half as large as its complement, angle b?

Answer 1

Angle A = 60º and Angle B = 30º

Explanation:

We know that A and B are complementary angles, therefore ∠A + ∠B =90. (+)

On the other hand, ∠A is half as large as ∠B; this can be written algebraically as
`A=(B)/(2)`. (*)

If we substitute (*) in (+) we get:

`(B)/(2)+B = 90\\\\ (B+2B=180)/(2) \\\\ B+2B=180\\\\ 3B=180\\\\ B=(180)/(3)\\\\ B=60`

And now we substitute the value of B in (+) and we get:

∠A+60 = 90

∠A = 90-60

∠A = 30