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Asked by Raghbendra Last Modified
Answer 
A quadrilateral can be split into 2 triangles. sum of internal angles of a quadrilateral is the sum of internal angles of 2 triangles, which is= 180+180=360°. this property holds true even if the quadrilateral is not convex. An example for non convex quadrilateral is shown in the figure below.
we can split quadrilateral ABCD in to two triangles ABC and ACD, hence sum of angles =180+180=360
read lessThe sum of the measures of the angles of a convex quadrilateral is 360° as a convex quadrilateral is made of two triangles.
Here, ABCD is a convex quadrilateral, made of two triangles ΔABD and ΔBCD. Therefore, the sum of all the interior angles of this quadrilateral will be same as the sum of all the interior angles of these two triangles i.e., 180º + 180º = 360º
Yes, this property also holds true for a quadrilateral which is not convex. This is because any quadrilateral can be divided into two triangles.
Here again, ABCD is a concave quadrilateral, made of two triangles ΔABD and ΔBCD. Therefore, sum of all the interior angles of this quadrilateral will also be 180º + 180º = 360º
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