Question

If the sum of the measures of interior angles of a regular convex polygon is 1620° how many sides does a polygon have find the measure of one interior angle and one exterior angle

Answer 1

Explanation:

(n-2)180=1620

n-2=1620/180=9

n=9+2=11

Answer 2

• the polygon has 11 sides
• one interior angle measures 147 3/11 degrees
• one exterior angle measures 32 8/11 degrees

Explanation:

The relation between the number of sides (n) and the total degree measure of interior angles is ...

angle total = 180° × (n -2)

We can find n by filling in the given total and solving:

1620 = 180(n -2)

1620/180 = 9 = n -2

9 + 2 = 11 = n

The number of sides is 11.

The measure of one interior angle is 1620°/11 = 147 3/11 degrees.

The measure of one exterior angle is 360°/11 = 32 8/11 degrees.