Question

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

Explanation:

Step1: Define variables

Let the measure of $\angle K$ be $x$ degrees. Then the measure of $\angle J$ is $x - 18$ degrees.

Step2: Use complementary angles property

Since $\angle J$ and $\angle K$ are complementary, their sum is $90^\circ$. So we have the equation:
$$(x - 18) + x = 90$$

Step3: Solve the equation

Combine like terms:
$$2x - 18 = 90$$
Add 18 to both sides:
$$2x = 90 + 18$$
$$2x = 108$$
Divide both sides by 2:
$$x = \frac{108}{2}$$
$$x = 54$$

Step4: Find the measure of $\angle J$

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

Answer:

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