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

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Solution

$A B C D$ is convex quadrilateral made of $2$ triangles $△ A B D$ and $△ B C D$ .
The property will held because the quadrilaterals are made of two triangles and sum of angles of interior angles of quadrilateral $=$ Sum of interior angles of two triangles.
Here, $A B C D$ is concave.
Sum of interior angles of quadrilateral $\Rightarrow 180 + 180$
$= 360$
[It is made of $2$ triangles]

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