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

## Answers

Answered by

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.

Answered by

3

**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

Similar questions