Question

Pentagon ABCDE is inscribed in a circle with centre O.

Statement (1): \[\angle \mathrm{AOB} = \frac{360^{\circ}}{5}\]

Statement (2): If pentagon is regular, \[\angle \mathrm{AOB} = \frac{360^{\circ}}{5}\]

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Statement 1 is false, and statement 2 is true.

Explanation:

Given, pentagon ABCDE is inscribed in a circle with center O.

If a pentagon is regular then the sides subtends equal angles at the center.

If ABCDE is a regular pentagon, then ∠AOB = \[\frac {360°}5​\].

∴ Statement 1 is false, and statement 2 is true.