Question

→lk bisects ∠jlm. if m∠jlk = (13x − 6)° and m∠klm = (11x + 2)°, what is m∠klm?
a) 45°
b) 44°
c) 46°
d) 92°

Explanation:

Step1: Use Angle Bisector Definition

Since \(\overrightarrow{LK}\) bisects \(\angle JLM\), we know that \(m\angle JLK = m\angle KLM\). So we set up the equation:
\(13x - 6 = 11x + 2\)

Step2: Solve for \(x\)

Subtract \(11x\) from both sides:
\(13x - 11x - 6 = 2\)
\(2x - 6 = 2\)

Add 6 to both sides:
\(2x = 2 + 6\)
\(2x = 8\)

Divide both sides by 2:
\(x = \frac{8}{2} = 4\)

Step3: Find \(m\angle KLM\)

Substitute \(x = 4\) into the expression for \(m\angle KLM\), which is \((11x + 2)^\circ\):
\(11(4) + 2 = 44 + 2 = 46^\circ\)

Answer:

C) \(46^\circ\)