Question

$\angle 1$ and $\angle 2$ are complementary angles. if $m\angle 1 = (4x + 20)\degree$ and $m\angle 2 = (3x + 7)\degree$, then find the measure of $\angle 1$.

Explanation:

Step1: Recall complementary angles sum to 90°

Complementary angles have a sum of \(90^\circ\). So, \(m\angle1 + m\angle2 = 90^\circ\). Substitute the given expressions: \((4x + 20) + (3x + 7) = 90\).

Step2: Solve for x

Combine like terms: \(4x + 3x + 20 + 7 = 90\) → \(7x + 27 = 90\). 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 \(m\angle1 = 4x + 20\): \(4(9) + 20 = 36 + 20 = 56\).

Answer:

The measure of \(\angle1\) is \(56^\circ\).