Question

Prove that the sum of all the angle of a quadrilateral is ${360}^{\circ }.$

Answer 1

To Prove: Sum of all angles of quadrilateral $={360}^{\circ }$

Sum of all angles of $n$-sided polygon $={180}^{\circ }(n-2)$ where $n$ is the number of sides of the polygon.

As we know that, a quadrilateral is a polygon with $4$ sides so, the sum of all angles will be,

$\text{Sum of angles}={180}^{\circ }(4-2)$

$={180}^{\circ }\times 2$

$={360}^{\circ }$

Hence Proved