Question

Two angles of a quadrilateral are 80${}^{\circ }$ and 160${}^{\circ }$. If the remaining two angles are equal, find the remaining angles.

• A. 180${}^{\circ }$
• B. 120${}^{\circ }$
• C. 90${}^{\circ }$
• D. 60${}^{\circ }$

Answer 1

The correct option is D

60${}^{\circ }$

A quadrilateral is a polygon having 4 sides.

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

Let the two remaining angles be $x^{\circ }$

$\Rightarrow$ 80${}^{\circ }$ + 160${}^{\circ }$ + $x^{\circ }$ + $x^{\circ }$ = 360${}^{\circ }$

$\Rightarrow$ $2x^{\circ }$ = 360${}^{\circ }$ - 240${}^{\circ }$

= 120${}^{\circ }$

$\Rightarrow$ $x$ = $\frac{120}{2}$

= 60

$\therefore$ The remaining two angles of given quadrilateral are 60${}^{\circ }$ each.