Question

In the figure below, m∠JKM = 73° , m∠LKM = 40°, and line KN bisects ∠LKM. Find m∠JKN.

Answer 1

From the diagram we can conclude:

`m\angle JKM=m\angle JKL+m\angle LKN+m\angle NKM`

Since KN bisects bisects ∠LKM:

`\begin{gathered} m\angle LKN=m\angle NKM \\ so\colon \\ m\angle LKM=2m\angle LKN \\ m\angle LKN=(m\angle LKM)/(2) \\ m\angle LKN=(40)/(2) \\ m\angle LKN=20 \end{gathered}`

Therefore:

`\begin{gathered} 73=m\angle JKL+20+20 \\ m\angle JKL=73-20-20 \\ m\angle JKL=33 \end{gathered}`

Hence:

`\begin{gathered} m\angle JKN=m\angle JKL+m\angle LKN \\ m\angle JKN=33+20 \\ m\angle JKN=53 \end{gathered}`