Question

1. xy using algebra ∠a and ∠b are complementary. the measure of ∠b is three times the measure of ∠a. find m∠a and m∠b.

Explanation:

Step1: Define variables and recall complementary angles

Let \( m\angle A = x \). Since \( \angle B \) is three times \( \angle A \), then \( m\angle B = 3x \). Complementary angles add up to \( 90^\circ \), so \( m\angle A + m\angle B = 90^\circ \).

Step2: Set up and solve the equation

Substitute the expressions for the angles into the equation: \( x + 3x = 90^\circ \). Combine like terms: \( 4x = 90^\circ \). Then solve for \( x \) by dividing both sides by 4: \( x=\frac{90^\circ}{4} = 22.5^\circ \).

Step3: Find \( m\angle B \)

Since \( m\angle B = 3x \), substitute \( x = 22.5^\circ \): \( m\angle B = 3\times22.5^\circ = 67.5^\circ \).

Answer:

\( m\angle A = 22.5^\circ \), \( m\angle B = 67.5^\circ \)