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(sum of interior angles = 180 (n-2) where n is the number of sides of the polygon)

1. if the sum of the interior angles of a polygon equals 1980, how many sides does the polygon have ?
2. how many degrees are there in the sum of the interior angles of a nine sides polygon ?
3. how many sides does a polygon have if the sum of its interior angles is 1620 ?
4. how many degrees are there in the sum of the interior angles of an eighteen sides polygon ?
5. how many degrees are there in the sum of the interior angles of a seventeen sides polygon ?
6. what is the sum of the interior angles of a quadrilateral ?

(i don't need an explanation, just the answers)

Respuesta :

Answer:

Step-by-step explanation:

The sum of the interior angles = 180 (n-2)

where n is the number of sides of the polygon.

1) if the sum of the interior angles of a polygon equals 1980,

180(n - 2) = 1980

180n - 360 = 1980

180n = 1980 + 360 = 2340

n = 2340/180 = 13

2) if n = 9, the number of degrees would be

180(n - 2) = 180(9 - 2)

= 180 × 7 = 1260 degrees

3) 180(n - 2) = 1620

n - 2 = 1620/180 = 9

n = 9 + 2 = 11

4) n = 18

The number of degrees would be

180(n - 2) = 180(18 - 2) = 2880 degrees.

5) n = 17

The number of degrees would be

180(n - 2) = 180(17 - 2) = 2700 degrees.

6) the sum of the interior angles of a quadrilateral is 360 degrees.

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