Question

1. if ∠k and ∠l are complementary angles. if m∠k=(2x - 10)° and m∠l=(10x + 4)°, find the measure of each angle.

Explanation:

Step1: Recall complementary - angles property

Complementary angles add up to 90°. So, \(m\angle K + m\angle L=90^{\circ}\).
Since \(m\angle K=(2x - 10)^{\circ}\) and \(m\angle L=(10x + 4)^{\circ}\), we have the equation \((2x - 10)+(10x + 4)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+10x-10 + 4=90\), which simplifies to \(12x-6 = 90\).

Step3: Solve for \(x\)

Add 6 to both sides of the equation: \(12x-6 + 6=90 + 6\), so \(12x=96\).
Then divide both sides by 12: \(x=\frac{96}{12}=8\).

Step4: Find \(m\angle K\)

Substitute \(x = 8\) into the expression for \(m\angle K\): \(m\angle K=(2x - 10)^{\circ}=(2\times8-10)^{\circ}=(16 - 10)^{\circ}=6^{\circ}\).

Step5: Find \(m\angle L\)

Substitute \(x = 8\) into the expression for \(m\angle L\): \(m\angle L=(10x + 4)^{\circ}=(10\times8+4)^{\circ}=(80 + 4)^{\circ}=84^{\circ}\).

Answer:

\(m\angle K = 6^{\circ}\), \(m\angle L=84^{\circ}\)