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Two angles summing to 180 degrees

Source: Tuymaada 2023 Junior P3

July 12, 2023
geometrycyclic quadrilateralreflectionTuymaada

Problem Statement

Point LL inside triangle ABCABC is such that CL=ABCL = AB and ∠BAC+∠BLC=180∘ \angle BAC + \angle BLC = 180^{\circ}. Point KK on the side ACAC is such that KL∥BCKL \parallel BC. Prove that AB=BKAB = BK
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