Question

km bisects ∠jkl. find m∠jkl
(diagram: point k with rays kj, km, kl; ∠jkm labeled 8x - 120, ∠lkm labeled 3x)

Explanation:

Step1: Use Angle Bisector Definition

Since \(\overrightarrow{KM}\) bisects \(\angle JKL\), \(\angle JKM=\angle MKL\). So \(8x - 120=3x\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(8x-3x - 120=3x-3x\), which simplifies to \(5x - 120 = 0\). Then add 120 to both sides: \(5x=120\). Divide both sides by 5: \(x = \frac{120}{5}=24\).

Step3: Find \(m\angle MKL\)

Substitute \(x = 24\) into \(3x\): \(m\angle MKL=3\times24 = 72^\circ\).

Step4: Find \(m\angle JKL\)

Since \(\angle JKL=\angle JKM+\angle MKL\) and \(\angle JKM=\angle MKL = 72^\circ\), then \(m\angle JKL=72^\circ+72^\circ = 144^\circ\).

Answer:

\(144^\circ\)