Question

1. ∠j and ∠k are complementary angles. the measure of ∠j is 18 less than the measure of ∠k. find the measure of each angle.

Explanation:

Step1: Set up equations

Let the measure of $\angle K=x$. Then the measure of $\angle J=x - 18$. Since $\angle J$ and $\angle K$ are complementary, $\angle J+\angle K = 90^{\circ}$. So, $(x - 18)+x=90$.

Step2: Simplify the equation

Combine like - terms: $x-18+x=90$ becomes $2x-18 = 90$.

Step3: Solve for $x$

Add 18 to both sides of the equation: $2x-18 + 18=90 + 18$, which gives $2x=108$. Then divide both sides by 2: $x=\frac{108}{2}=54$.

Step4: Find the measure of $\angle J$

Substitute $x = 54$ into the expression for $\angle J$. $\angle J=x - 18=54-18 = 36$.

Answer:

The measure of $\angle J$ is $36^{\circ}$ and the measure of $\angle K$ is $54^{\circ}$.