In the given problem, we know the following:
-
Angles A and B are complementary, which means that their measures add up to 90 degrees: \[ m∠A + m∠B = 90° \]
-
You are given that \( m∠A = x° \) and \( m∠B = 2x° \).
Substituting the expressions for angles A and B into the complementary angle equation, we get: \[ x + 2x = 90° \] \[ 3x = 90° \] Dividing both sides by 3: \[ x = 30° \]
Now, we can find the measure of \( m∠B \): \[ m∠B = 2x = 2(30°) = 60° \]
Thus, the measure of ∠B is 60°.