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MathNet 2019-part-01 — 184 problems (EN–VI) Question 181

Math Olympiad Vault · MathNet 2019-part-01 — 184 problems (EN–VI)

Question 181

The angle $ADC$ of the parallelogram $ABCD$ equals $40^\circ$. The point $K$ is given such that the segments $AK$ and $BC$ intersect, $AK = BC$ and $\angle BAK = 80^\circ$. The point $L$ is given such that the segments $CL$ and $AD$ intersect, $CL = AB$ and $\angle BCL = 80^\circ$.
Find the angles of the triangle $BKL$.