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What is the sum of the measures of the angles of a convex quadrilateral? Why this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)

Answer»

Solution: Angle sum of a convex quadrilateral = (4 – 2) x 180⁰ = 2 x 180⁰ = 360⁰
Since, quadrilateral, which is not convex, i.e. concave has same number of sides i.e. 4 as a convex quadrilateral have, thus, a quadrilateral which not convex also hold this property. i.e. angle some of a concave quadrilateral is also equal to 360⁰


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