Question

8 fill in the blank 2 points ∠k and ∠l are complementary angles. if m∠k=(3x + 3)° and m∠l=(10x - 4)°, find the measure of each angle. m∠k = type your answer... ° m∠l = type your answer... °

Explanation:

Step1: Recall complementary - angle property

Complementary angles add up to 90°. So, \(m\angle K + m\angle L=90^{\circ}\).
Substitute \(m\angle K=(3x + 3)^{\circ}\) and \(m\angle L=(10x - 4)^{\circ}\) into the equation: \((3x + 3)+(10x - 4)=90\).

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

Step4: Find \(m\angle K\)

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

Step5: 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:

\(m\angle K = 24\)
\(m\angle L = 66\)