Question

Angle addition and angle bisectors

In the figure below, mLJKM = 103°, mLNKM
=
32°, and KN bisects LLKM. Find mLJKL.

Answer 1

∠ JKL = 39°

Explanation:

since KN bisects ∠ LKM , then

∠ LKN = ∠ NKM = 32°

from the diagram

∠ JKL + ∠ LKN + ∠ NKM = ∠ JKM , that is

∠ JKL + 32° + 32° = 103°

∠ JKL + 64° = 103° ( subtract 64° from both sides )

∠ JKL = 39°