Question

What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex?

• A. ${360}^o$, No
• B. ${360}^o$, Yes
• C. ${180}^o$, No
• D. ${180}^o$, Yes

Answer 1

The correct option is B ${360}^o$, Yes

The sum of the measures of the angles of a convex quadrilateral is 360 as a convex quadrilateral is made of two triangles.
If ABCD is a convex quadrilateral, made of two triangles ABD and BCD. 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.