Question

which of the following statements is true? answer attempt 1 out of 3 m∠kln = 2(m∠mln) 1/2(m∠klm)=m∠kln 1/2(m∠kln)=m∠mln m∠klm = m∠kln

Explanation:

Step1: Recall angle - bisector property

An angle - bisector divides an angle into two equal angles. If $\overrightarrow{LN}$ is the angle - bisector of $\angle KLM$, then $m\angle KLN=m\angle MLN$ and $m\angle KLM = 2m\angle KLN=2m\angle MLN$.

Step2: Analyze each option

• Option 1: $m\angle KLN = 2(m\angle MLN)$ is incorrect because if $\overrightarrow{LN}$ is the angle - bisector of $\angle KLM$, then $m\angle KLN=m\angle MLN$.
• Option 2: $\frac{1}{2}(m\angle KLM)=m\angle KLN$ is correct. Since $\overrightarrow{LN}$ bisects $\angle KLM$, $\angle KLM$ is divided into two equal angles $\angle KLN$ and $\angle MLN$, so $m\angle KLM = 2m\angle KLN$, which implies $\frac{1}{2}(m\angle KLM)=m\angle KLN$.
• Option 3: $\frac{1}{2}(m\angle KLN)=m\angle MLN$ is incorrect. Since $m\angle KLN=m\angle MLN$, $\frac{1}{2}(m\angle KLN)

eq m\angle MLN$.

• Option 4: $m\angle KLM = m\angle KLN$ is incorrect. Since $m\angle KLM = 2m\angle KLN$, $m\angle KLM

eq m\angle KLN$.

Answer:

$\frac{1}{2}(m\angle KLM)=m\angle KLN$