Question

If all the angles of a 14-sided figure are equal, then the measure of each angle is equal to ?

• A. ${\left(184\frac{2}{7}\right)}^{\circ }$
• B. ${\left(164\frac{2}{7}\right)}^{\circ }$
• C. ${\left(134\frac{2}{7}\right)}^{\circ }$
• D. ${\left(154\frac{2}{7}\right)}^{\circ }$

Answer 1

Answer: (D)

${\left(154\frac{2}{7}\right)}^{\circ }$

Given, all the angles of a 14-sided figure are equal.

That figure must be a polygon.
Sum of all angles of a polygon = ${180}^o(n-2)$

where,

$n$ = number of sides of a polygon

$\therefore$ $m\left(angle\right)$ = $\frac{{180}^o(n-2)}{n}$ = $\frac{{180}^o(14-2)}{14}$

= $\frac{{180}^o\times 12}{14}$ = ${\left(154\frac{2}{7}\right)}^{\circ }$