Angle addition and angle bisectors In the figure below, mLJKM = 90°, mLNKM = 23°, and KN bisects LLKM. Find mLJKL.
Mathematics
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Question
Angle addition and angle bisectors
In the figure below, mLJKM = 90°, mLNKM
=
23°, and KN bisects LLKM. Find mLJKL.
In the figure below, mLJKM = 90°, mLNKM
=
23°, and KN bisects LLKM. Find mLJKL.
1 Answer

1. User Answers sqdancefan
Answer:
∠JKL = 44°
Stepbystep 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°.