Question

what is the sum of the measure of the angle of a convex quadrilateral will this property hold in the quadrilateral nonconvex​

Answer 1

Answer:

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

In above convex quadrilateral, it made of two triangles. 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

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, above concave quadrilateral is made of two triangles. Therefore, sum of all the interior angles of this quadrilateral will also be 180º + 180º = 360º