Question

1. angles j and k are supplementary. the measure of ∠k is nine times the measure of ∠j. determine the measure of each of the two angles.

Explanation:

Step1: Set up equations

Let the measure of $\angle J=x$. Then the measure of $\angle K = 9x$. Since $\angle J$ and $\angle K$ are supplementary, $x + 9x=180^{\circ}$.

Step2: Solve the equation

Combining like - terms, we get $10x = 180^{\circ}$. Dividing both sides by 10, $x=\frac{180^{\circ}}{10}=18^{\circ}$.

Step3: Find the measure of $\angle K$

Since $\angle K = 9x$, substituting $x = 18^{\circ}$, we have $\angle K=9\times18^{\circ}=162^{\circ}$.

Answer:

The measure of $\angle J$ is $18^{\circ}$ and the measure of $\angle K$ is $162^{\circ}$.