Question

1. two angles, ∠a and ∠b, are complementary. the measure of ∠a is 67°. write and solve an equation to determine the measure of ∠b. check your solution.

Explanation:

Step1: Recall complementary angles

Complementary angles sum to $90^\circ$. So, $\angle A + \angle B = 90^\circ$.

Step2: Substitute $\angle A = 67^\circ$

We get the equation $67^\circ + \angle B = 90^\circ$.

Step3: Solve for $\angle B$

Subtract $67^\circ$ from both sides: $\angle B = 90^\circ - 67^\circ = 23^\circ$.

Step4: Check the solution

Add $\angle A$ and $\angle B$: $67^\circ + 23^\circ = 90^\circ$, which confirms they are complementary.

Answer:

The measure of $\angle B$ is $23^\circ$.