Question

∠1 and ∠2 are complementary angles. if ( mangle1 = (4x + 20)^circ ) and ( mangle2 = (3x + 7)^circ ), then find the measure of ( angle1 ).

Explanation:

Step1: Recall complementary angles sum to 90°

Since \( \angle 1 \) and \( \angle 2 \) are complementary, \( m\angle 1 + m\angle 2 = 90^\circ \). Substitute the given expressions: \( (4x + 20) + (3x + 7) = 90 \).

Step2: Solve for x

Combine like terms: \( 7x + 27 = 90 \). Subtract 27 from both sides: \( 7x = 90 - 27 = 63 \). Divide by 7: \( x = \frac{63}{7} = 9 \).

Step3: Find \( m\angle 1 \)

Substitute \( x = 9 \) into \( m\angle 1 = 4x + 20 \): \( 4(9) + 20 = 36 + 20 = 56 \).

Answer:

\( 56 \)