Question

1. ∠k and ∠l are complementary angles. if ( mangle k = (3x + 3)^circ ) and ( mangle l = (10x - 4)^circ ), find the measure of each angle.

Explanation:

Step1: Recall complementary angles sum to \(90^\circ\)

Since \(\angle K\) and \(\angle L\) are complementary, \(m\angle K + m\angle L = 90^\circ\). Substitute the given expressions: \((3x + 3) + (10x - 4) = 90\).

Step2: Solve for \(x\)

Combine like terms: \(3x + 10x + 3 - 4 = 90\) → \(13x - 1 = 90\). Add 1 to both sides: \(13x = 91\). Divide by 13: \(x = 7\).

Step3: Find \(m\angle K\)

Substitute \(x = 7\) into \(m\angle K = 3x + 3\): \(3(7) + 3 = 21 + 3 = 24^\circ\).

Step4: Find \(m\angle L\)

Substitute \(x = 7\) into \(m\angle L = 10x - 4\): \(10(7) - 4 = 70 - 4 = 66^\circ\).

Answer:

\(m\angle K = 24^\circ\), \(m\angle L = 66^\circ\)