Question

1. ∠l and ∠m are complementary, ( m∠l = 2x + 25 ), and ( m∠m = 4x + 11 ). determine the measure of each angle.

Explanation:

Step1: Use the definition of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \(m\angle L + m\angle M=90\).
Substitute \(m\angle L = 2x + 25\) and \(m\angle M = 4x + 11\) into the equation:
\((2x + 25)+(4x + 11)=90\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+4x+25 + 11=90\), which gives \(6x+36 = 90\)

Step3: Solve for \(x\)

Subtract 36 from both sides: \(6x=90 - 36\), so \(6x=54\)
Divide both sides by 6: \(x=\frac{54}{6}=9\)

Step4: Find \(m\angle L\)

Substitute \(x = 9\) into \(m\angle L=2x + 25\): \(m\angle L=2\times9+25=18 + 25=43^{\circ}\)

Step5: Find \(m\angle M\)

Substitute \(x = 9\) into \(m\angle M=4x + 11\): \(m\angle M=4\times9+11=36+11 = 47^{\circ}\)

Answer:

\(m\angle L = 43^{\circ}\) and \(m\angle M=47^{\circ}\)