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draw a line xy parallel to ab at vertex b,
∠cab = ∠abx (co-interior angles)
∠acb = ∠cby (co-interior angles)
∠abc + ∠cby + ∠abx =180°
therefore, ∠cab + ∠acb + ∠abc =180°
angle sum of a triangle = 180°
sum of angles of two triangles = 180° +180° = 360°
therefore angle sum of quadrilateral = 360°
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