Question

The sum of all angles of a quadrilateral is
(a) ${180}^{\circ }$
(b) ${270}^{\circ }$
(c) ${360}^{\circ }$
(d) ${480}^{\circ }$

Answer 1

Let $ABCD$ is a Quadrilateral.

$\angle A,\angle B,\angle C$ and $\angle D$ are the angles of Quadrilateral.

$BD$ is a diagonal.

In figure,

Diagonal $BD$ divides the quadrilateral into two triangles.

$\Rightarrow$ Sum of the angle of quadrilateral $ABCD=$ Sum of the angles of $△ADC+$ Sum of the angles of $△BDC$

$\Rightarrow \angle A+\angle B+\angle C+\angle D$

$=(\angle x+\angle y+\angle u)+(\angle z+\angle w+\angle v)$

$={180}^{\circ }+{180}^{\circ }$ [Since, Sum of the angles of a triangle is ${180}^{\circ }$]

$={360}^{\circ }$

$\Rightarrow \angle A+\angle B+\angle C+\angle D={360}^{\circ }$

Therefore, the sum of all angles of a quadrilateral is ${360}^{\circ }$.

Hence, Option C is correct.