Question

$\angle 1$ and $\angle 2$ are complementary angles. if $m\angle 1 = (4x + 3)^\circ$ and $m\angle 2 = (3x + 24)^\circ$, then find the measure of $\angle 1$.

Explanation:

Step1: Recall complementary angles sum to 90°

Since ∠1 and ∠2 are complementary, \( m\angle1 + m\angle2 = 90^\circ \). Substitute the given expressions: \( (4x + 3) + (3x + 24) = 90 \).

Step2: Simplify and 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 \( m\angle1 \)

Substitute \( x = 9 \) into \( m\angle1 = (4x + 3)^\circ \): \( 4(9) + 3 = 36 + 3 = 39 \).

Answer:

\( 39^\circ \)