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QuestionFind the measures of complementary angles ∠J\angle J and ∠K\angle K, where ∠J\angle J is 18 less than ∠K\angle K.

Studdy Solution

STEP 1

Assumptions1. ∠J\angle J and ∠K\angle K are complementary angles. This means that the sum of the measures of these two angles is90 degrees. . The measure of ∠J\angle J is18 less than the measure of ∠K\angle K.

STEP 2

Let's denote the measure of ∠K\angle K as xx. According to the problem, the measure of ∠J\angle J is18 less than the measure of ∠K\angle K, so we can denote the measure of ∠J\angle J as x−18x -18.

STEP 3

Since ∠J\angle J and ∠K\angle K are complementary, their measures add up to90 degrees. We can write this as an equationx+(x−18)=90x + (x -18) =90

STEP 4

implify the equation by combining like terms.
2x−18=902x -18 =90

STEP 5

Add18 to both sides of the equation to isolate the term with xx.
2x=90+182x =90 +18

STEP 6

Calculate the right side of the equation.
2x=1082x =108

STEP 7

Divide both sides of the equation by2 to solve for xx.
x=1082x = \frac{108}{2}

STEP 8

Calculate the value of xx.
x=54x =54So, the measure of ∠K\angle K is54 degrees.

STEP 9

Substitute x=54x =54 into the expression for the measure of ∠J\angle J.
∠J=x−18=54−18\angle J = x -18 =54 -18

STEP 10

Calculate the measure of ∠J\angle J.
∠J=36\angle J =36So, the measure of ∠J\angle J is36 degrees.
The measure of ∠J\angle J is36 degrees and the measure of ∠K\angle K is54 degrees.

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