Question

km bisects ∠jkl. find m∠jkl.

Explanation:

Step1: Recall angle bisector definition

Since \( \overrightarrow{KM} \) bisects \( \angle JKL \), \( \angle JKM = \angle MKL \). So \( 8x - 130 = 3x \).

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides: \( 8x - 3x - 130 = 0 \) → \( 5x - 130 = 0 \).
Add 130 to both sides: \( 5x = 130 \).
Divide by 5: \( x = \frac{130}{5} = 26 \).

Step3: Find \( m\angle MKL \)

Substitute \( x = 26 \) into \( 3x \): \( 3(26) = 78 \).

Step4: Find \( m\angle JKL \)

Since \( \angle JKL = \angle JKM + \angle MKL \) and \( \angle JKM = \angle MKL = 78^\circ \), \( m\angle JKL = 78 + 78 = 156^\circ \).

Answer:

\( 156^\circ \)