Question

What's is the sum of the measure of the angels of a convex quadrilateral? will this property hold if the quadrilateral is not convex ?(make a non convex quadrilateral and try​

Answer 1

The sum of the measures of the angles of a convex quadrilateral is 360° as a convex quadrilateral is made of two triangles.

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Here, ABCD is a convex quadrilateral, made of two triangles ABC and ABCD. 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., 180° + 180° = 360°

Yes, this property also holds true for a quadrilateral which is not convex. This is because any quadrilateral can be divided into two triangles.

( Refer to the first attachment )

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Here again, ABCD is a concave quadrilateral, made of two triangles ABC and ABCD. Therefore, sum of all the interior angles of this quadrilateral will also be 180° + 180° = 360°

( Refer to the second attachment )