Question

The sum of the measures of the interior angles of a convex polygon is 1800 degrees? How many sides does the

polygon have?

Answer 1

12 sides

Explanation:

Given

Sum of interior angle = 1800 degrees

Required

Number of sides of the polygon

The sum of interior of a convex polygon is calculated using the following formula:

Sum = (n - 2) * 180

Where n is the number of sides of the polygon.

By substituting 1800 for Sum, we have

`1800 = (n - 2) * 180`

Divide through by 180

`(1800)/(180) = ((n - 2) * 180)/(180)`

`10 = n - 2`

Add 2 to both sides

`10 + 2 = n - 2 + 2`

`12 = n`

Re order

`n = 12`

Hence, the number of sides of the polygon is 12