Find the number of sides of a regular polygon if its each interior ang

1.	Find the number of sides of a regular polygon if its each interior angle is 165°.
Answer» Each interior angle = 165° ∴ Each exterior angle = 180° – 165° = 15° Let the number of sides be n. Sum of all exterior angles of polygon = 360° ∴ Value of each angle = 360°/n According to question = 360°/n = 15° ⇒ n = 360°/15° = 24 Therefore, the number of sides be 24

Find the number of sides of a regular polygon if its each interior angle is 165°.

Answer»

Each interior angle = 165°

∴ Each exterior angle = 180° – 165° = 15°

Let the number of sides be n.

Sum of all exterior angles of polygon = 360°

∴ Value of each angle = 360°/n

According to question = 360°/n = 15°

⇒ n = 360°/15° = 24

Therefore, the number of sides be 24