Question

If two interior angles of a hexagon are 70${}^{\circ }$ and 50${}^{\circ }$ and all the remaining interior angles are equal to $x^{\circ }$ then this hexagon is a concave polygon.

• A. True
• B. False

Answer 1

The correct option is B

False

A hexagon is a polygon of 6 sides and 6 angles.

$\because$ Sum of interior angles of a 'n' sided polygon = (n-2) $\times$ 180 ${}^{\circ }$

$\Rightarrow$ Sum of the interior angles of a hexagon = (6-2) $\times$180${}^{\circ }$

= 720${}^{\circ }$

Given two interior angles of a hexagon are 70${}^{\circ }$ and 50${}^{\circ }$ and remaining angles are $x^{\circ }$.

$\Rightarrow$ 70${}^{\circ }$ + 50${}^{\circ }$ + $x^{\circ }$ + $x^{\circ }$ + $x^{\circ }$ + $x^{\circ }$ = 720${}^{\circ }$

$\Rightarrow$ 120${}^{\circ }$ + $4x$${}^{\circ }$ = 720${}^{\circ }$

$\Rightarrow$ $4x$${}^{\circ }$ = 600${}^{\circ }$

$\Rightarrow$ $x^{\circ }$ = 150${}^{\circ }$

Now the angles of this hexagon are 70${}^{\circ }$, 50${}^{\circ }$ and remaining angles are 150${}^{\circ }$. Since all the angles of the polygon are less than 180${}^{\circ }$, it is a convex polygon.