Question

The sides of a regular octagon are produced to form a star. The measure of the angle at each point of the star is

• A. ${55}^o$
• B. ${65}^o$
• C. ${75}^o$
• D. ${90}^o$

Answer 1

The correct option is D ${90}^o$

$8$ angles form a star
$=$ $(2n-8)\times {90}^{\circ }$
where $n=$ $8$
$=$ $\left[2\right(8)-8]\times {90}^{\circ }$
$=$ $8\times {90}^{\circ }$
Since it is a regular octagon, so each angle
$=$ $\frac{8\times {90}^{\circ }}{8}$ $=$ ${90}^{\circ }$