Question

finding angles ∠a and ∠b are complementary. find ( mangle a ) and ( mangle b ).
( mangle a = (3x + 2)^circ )
( mangle b = (x - 4)^circ )
( mangle a = square^circ )
( mangle b = square^circ )

Explanation:

Step1: Recall complementary angles sum to 90°

Since \( \angle A \) and \( \angle B \) are complementary, \( m\angle A + m\angle B = 90^\circ \). Substitute the given expressions: \( (3x + 2) + (x - 4) = 90 \).

Step2: Solve for \( x \)

Simplify the left side: \( 3x + 2 + x - 4 = 90 \) → \( 4x - 2 = 90 \). Add 2 to both sides: \( 4x = 92 \). Divide by 4: \( x = 23 \).

Step3: Find \( m\angle A \)

Substitute \( x = 23 \) into \( m\angle A = (3x + 2)^\circ \): \( 3(23) + 2 = 69 + 2 = 71^\circ \).

Step4: Find \( m\angle B \)

Substitute \( x = 23 \) into \( m\angle B = (x - 4)^\circ \): \( 23 - 4 = 19^\circ \).

Answer:

\( m\angle A = 71^\circ \)
\( m\angle B = 19^\circ \)