Question

In the given figure, ABCDEFG is a regular polygon. The measure of $7(\angle EOD+\angle FOG)$ is equal to

• A.
  ${360}^{\circ }$
• B.
  ${720}^{\circ }$
• C.
  ${180}^{\circ }$
• D.
  ${500}^{\circ }$

Answer 1

The correct option is B

${720}^{\circ }$
In ABCDEFG, each central angle will be equal as it is a regular polygon.

Let each central angle be x.



$\therefore 7x={360}^{\circ }\Rightarrow x={\left(\frac{360}{7}\right)}^{\circ }Consider:7(\angle EOD+\angle FOG)=7(x+x)=7\left(2x\right)=14x=14\times {\left(\frac{360}{7}\right)}^{\circ }=2\times {360}^{\circ }={720}^{\circ }$

Hence, the correct answer is option (b).