Question

1. ∠k and ∠l are complementary angles. if m∠k=(3x + 3)° and m∠l=(10x - 4)°, find the measure of each angle.

Explanation:

Step1: Recall complementary - angle property

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

Step2: Simplify the left - hand side

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: $13x-1 + 1=90 + 1$, giving $13x=91$.
Divide both sides by 13: $x=\frac{91}{13}=7$.

Step4: Find the measure of $\angle K$

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 the measure of $\angle L$

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:

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