Question

Prove that all four angles of a quadrilateral cannot be obtuse angles.

Answer 1

$\Rightarrow$ We know that quadrilateral contains 4 sides.

$\Rightarrow$ So, sum of all it's interior angles is ${360}^{\circ }$

$\Rightarrow$ We know that an angle which is greater than ${90}^{\circ }$ is called obtuse angle.

$\Rightarrow$ If all angles in quadrilateral are greater than ${90}^{\circ }$ then sum of all it's interior angles will not be equal to ${360}^{\circ }$, it will be greater than ${360}^{\circ }$. So, all four angles of quadrilateral should not be obtuse angle.

$\Rightarrow$ Hence, We have proved that all four angles of quadrilateral cannot be obtuse angles.