Question

The interior angle of a regular pentagon is four times the exterior angle of a regular decagon. State the whether the given statement is correct or not.

• A. True
• B. False

Answer 1

The correct option is B

False

Interior angle of a regular pentagon

$=\frac{(2n-4)}{n}\times {90}^{\circ }=\left(\frac{6}{5}\right)\times {90}^{\circ }={108}^{\circ }Exteriorangleofregulardecagon={180}^{\circ }-\frac{(2n-4)}{n}\times {90}^{\circ }={180}^{\circ }-\left(\frac{16}{10}\right)\times {90}^{\circ }={180}^{\circ }-{144}^{\circ }={36}^{\circ }So,{108}^{\circ }=3\times {36}^{\circ }$

It is three times the exterior angle of a regular decagon. Hence, given statement is false.