Question

the measure of angle jkl can be represented using the expression 3x + 5
what is the degree measure of \angle jkl?

Explanation:

Step1: Establish equation

Since \( \angle JKL = 3x + 5 \), and \( \angle JKM = 45^{\circ} \), \( \angle MKL=x^{\circ} \), and \( \angle JKL=\angle JKM+\angle MKL \), we have \( 3x + 5=45 + x \).

Step2: Solve for \( x \)

Subtract \( x \) from both sides: \( 3x - x+5=45 + x - x \), so \( 2x+5 = 45 \).
Subtract \( 5 \) from both sides: \( 2x+5 - 5=45 - 5 \), so \( 2x=40 \).
Divide both sides by \( 2 \): \( x = 20 \).

Step3: Find \( \angle JKL \)

Substitute \( x = 20 \) into \( 3x + 5 \): \( 3\times20+5=60 + 5=71 \).

Answer:

\( 71 \)