Question

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

Explanation:

Step1: Apply Angle Addition Postulate

According to the Angle Addition Postulate, \( \angle JKL=\angle JKM + \angle MKL\). 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 the expression for \( \angle JKL\) (\(3x + 5\)).
\(3x+5=3\times20 + 5=60 + 5=65\).

Answer:

\(65\)