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

Answer:

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

Step-by-step 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:

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