Mathematics

Question

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

1 Answer

  • Answer:

      ∠JKL = 44°

    Step-by-step 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°.

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