Polygon Math Example 4

Follow the full solution, then compare it with the other examples linked below.

hard

A polygon has an interior angle sum of

1980°

. How many sides does it have?

1
Step 1: $(n-2) \times 180 = 1980$ .
2
Step 2: $n-2 = 1980/180 = 11$ , so $n = 13$ .
3
Step 3: Check: a 13-gon has interior angle sum $(13-2)\times 180 = 11\times 180 = 1980°$ . Confirmed.

Answer

13 sides (tridecagon)

Solving

(n-2)\times 180 = S

for

n

gives

n = S/180 + 2

. For any integer

n \geq 3

, a regular

n

-gon exists. A regular 13-gon has each interior angle

1980°/13 \approx 152.3°

About Polygon

A closed two-dimensional figure formed by three or more straight line segments connected end-to-end.

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