Question

If one interior angle of an octagon is ${310}^{\circ }$ and each of the other angles are $x^{\circ }$, then x = ___

• A. ${180}^{\circ }$
• B. ${130}^{\circ }$
• C. ${140}^{\circ }$
• D. ${110}^{\circ }$

Answer 1

The correct option is D

${110}^{\circ }$

An octagon is a polygon having 8 sides.

$\because$ The sum of interior angles of a polygon having 'n' sides is (2n - 4) $\times$ 90${}^{\circ }$.

$\therefore$ Sum of interior angles of an octagon = $(16-4)\times {90}^{\circ }$

$\Rightarrow$ 310${}^{\circ }$ + 7$x$${}^{\circ }$ = $12\times {90}^{\circ }$

$\Rightarrow$ 7$x^{\circ }$ = 1080${}^{\circ }$ - 310${}^{\circ }$

$\Rightarrow$ $7x^{\circ }$ = 770${}^{\circ }$

$\Rightarrow$ $x={110}^{\circ }$