Find the measure of angle LMK

Geometry Level 3

The point $M$ inside the $\triangle KLM$ is such that $KL=JK$ , $\angle LJM=30 \degree$ , $\angle MKJ=37.5 \degree$ , and $\angle JKL=50 \degree$ . Find the measure of $\angle LMK$ in degrees.

The answer is 150.

1 solution

Maria Kozlowska
Apr 18, 2021

$KN \perp JL$

$\angle NKM = \angle MKL=12.5 \degree$ $\angle LNM = \angle MNK=60 \degree$ Therefore $\angle NLM = \angle MLK=17.5 \degree$ Therefore

$\angle LMK =150 \degree$

Find the measure of angle LMK

The answer is 150.

1 solution

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