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: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \(m\angle K + m\angle L=90^{\circ}\).
Substitute the given expressions: \((3x + 3)+(10x-4)=90\).

Step2: Simplify the left - hand side of the equation

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

Step3: Solve for \(x\)

Add \(1\) to both sides: \(13x-1 + 1=90 + 1\), so \(13x=91\).
Divide both sides by \(13\): \(x=\frac{91}{13}=7\).

Step4: Find \(m\angle K\)

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

Step5: Find \(m\angle L\)

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

Answer:

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