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: Set up the equation for complementary angles

Complementary angles sum to \(90^{\circ}\). So, \((3x + 3)+(10x-4)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(3x+10x+3 - 4=90\), which gives \(13x-1 = 90\).

Step3: Solve for \(x\)

Add \(1\) to both sides: \(13x=90 + 1=91\). Then divide by \(13\): \(x=\frac{91}{13}=7\).

Step4: Find the measure of \(\angle K\)

Substitute \(x = 7\) into \(m\angle K=(3x + 3)^{\circ}\). So, \(m\angle K=(3\times7+3)^{\circ}=(21 + 3)^{\circ}=24^{\circ}\).

Step5: Find the measure of \(\angle L\)

Substitute \(x = 7\) into \(m\angle L=(10x-4)^{\circ}\). So, \(m\angle L=(10\times7-4)^{\circ}=(70-4)^{\circ}=66^{\circ}\).

Answer:

\(m\angle K = 24^{\circ}\) and \(m\angle L=66^{\circ}\)