Question

<A and <B
are complementary angles. The measure of <A
is twice the measure of <B.


Write and equation to represent the complementary angle relationship between <A
and <B.
Use the equation to find the measure of <A
and <B.
Show all of your work.


WRITER

Answer 1

Let m∠A = A and m∠B = B (in degrees).

1. Complementary angles: A + B = 90.
2. Given: A = 2B.

Substitute (2) into (1):
2B + B = 90
3B = 90
B = 90 ÷ 3 = 30°

Then A = 2B = 2(30°) = 60°.

Check: 60° + 30° = 90°, so they are complementary.

Answer: m∠A = 60°, m∠B = 30°.