Question

the measure of angle jkl can be represented using the expression 3x + 5. what is the degree measure of ∠jkl? 45° x°

Explanation:

Step1: Use the property of adjacent angles

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

Step2: Solve the equation for \(x\)

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

Step3: Find the measure of \(\angle JKL\)

Substitute \(x = 20\) into \(3x + 5\). Then \(3\times20+5=60 + 5=65\).

Answer:

\(65\)