Question

The three angles of a quadrilateral are ${40}^{\circ },{80}^{\circ },{90}^{\circ }$. The fourth angle is:

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

A quadrilateral is a polygon having 4 sides.

$\because$ The sum of interior angles of a polygon having 'n' sides is (n-2) $\times$ 180${}^{\circ }$.

$\therefore$ sum of interior angles of a quadrilateral= 360 ${}^o$

Given, angles of quadrilateral are ${40}^{\circ },{80}^{\circ },{90}^{\circ }$. Let the fourth angle be $x^{\circ }$

$\Rightarrow$ 80${}^{\circ }$ + 40${}^{\circ }$ + ${90}^{\circ }$ + $x^{\circ }$ = 360${}^{\circ }$

$\Rightarrow$ $x^{\circ }$ = 360${}^{\circ }$ - 210${}^{\circ }$

= 150${}^{\circ }$

$\therefore$ The fourth angle of the quadrilateral is 150${}^{\circ }$.