Question

Angle addition and angle bisectors

In the figure below, mLJKM = 90°, mLNKM
=
23°, and KN bisects LLKM. Find mLJKL.

Answer 1

∠JKL = 44°

Explanation:

You want the measure of angle JKL, when ∠JKM = 90° and KN bisects ∠LKM to give ∠NKM = 23°.

Angle bisector

An angle bisector creates two congruent angles:

∠LKN = ∠NKM = 23°

Angle sum

An angle is equal to the sum of its parts:

∠JKL +∠LKN +∠NKM = ∠JKM

∠JKL +23° +23° = 90°

∠JKL = 90° -46° = 44°

The measure of ∠JKL is 44°.