Question

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

Explanation:

Step1: Recall complementary - angle property

Complementary angles sum to 90°. So, \(m\angle K + m\angle L=90^{\circ}\).

Step2: Substitute the given angle - measures

Substitute \(m\angle K=(3x + 3)^{\circ}\) and \(m\angle L=(10x-4)^{\circ}\) into the equation: \((3x + 3)+(10x-4)=90\).

Step3: Simplify the left - hand side of the equation

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

Step4: Solve for \(x\)

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

Step5: Find \(m\angle K\)

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

Step6: Find \(m\angle L\)

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

Answer:

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