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

Answer 1

∠A = 60

∠B = 30

Complementary angles are angles that add up to 90 degrees, and the measure of ∠A is twice as much as ∠B

60 + 30 = 90

60 / 30 = 2

60 / 2 = 30

Explanation:

The other answer is still correct, just thought I'd make it simpler.

Hope this helps!

Answer 2

`\text{Equation: }2\angle B+\angle B=90\\\angle A=60^(\circ),\\\angle B=30^(\circ)`

Explanation:

Complimentary angles are angles that add up to 90 degrees. Therefore, we can write the following system of equations:

`\begin{cases}\angle A=2\angle B,\\\angle A+\angle B=90\end{cases}`

Solving, we obtain the equation:

`2\angle B+\angle B=90,\\3\angle B=90,\\\angle B=\boxed{30^(\circ)}`

Plugging this back in to our first equation, we get:

`\angle A=2(30)=\boxed{60^(\circ)}`