Question

Construct a regular pentagon inside a circle of radius $6cm$. The angle subtended by each side at the centre of the circle is:

• A. ${108}^{\circ }$
• B. ${54}^{\circ }$
• C. ${72}^{\circ }$
• D. ${144}^{\circ }$

Answer 1

The correct option is C ${72}^{\circ }$

Total angle subtended by five sides at the centre is ${360}^{\circ }$.

So angle subtended by one side at the centre is $\frac{1}{5}{.360}^{\circ }={72}^{\circ }$

The angle subtended by each side at the centre of the circle is ${72}^{\circ }$

So the correct answer is option C.