Question

Will angle sum property work if the quadrilateral is not convex

Answer 1

We found a similar question to the one that you posted. Please check it out here.

Angle sum property =>the sum of mearures of the angles of a convex quadrilateral in 360∘
Yes,even if quadrilateral is not convex then, the angle sum property can be applied.

Let ABCD is a non – convex quadrilateral and join BD, which also divides the quadrilateral in two triangles.
Using angle sum property of triangle,
InΔABD,∠1+∠2+∠3=180∘......(i)InΔBDC,∠4+∠5+∠6=180∘......(ii).Addingeq.(i)and(ii),∠1+∠2+∠3+∠4+∠5+∠6=360∘⇒∠1+∠2+(∠3+∠4)+∠5+∠6=360∘
Hence proved.