Question

Each interior angle of a polygon is 108. How many sides does it have?

Answer 1

Answer:

Each interior angle of the polygon is 108 degrees, so each exterior angle of the polygon is 180-108 = 72 degrees. So the number of sides is 360/72 = 5.

Answer 2

Answer:

★If n is the number of sides, each interior angle I can be calculated by the following formula:

⇒I = 180(n - 2)/n

❥︎Substitute:

⇒108 = 180(n - 2)

❥︎Multiply both sides by n:

⇒108n = 180(n - 2)

❥︎Distribute:

⇒108n = 180n - 360

❥︎Subtract 180n from both sides:

⇒108n - 180n = -360

❥︎Combine like terms:

⇒-72n = -360

❥︎Divide both sides by -72:

⇒n = 5