Question 18 (5 points) Determine the sum of the measures of the interior angles of a dodecagon (12-sided
polygon).
540°
1,800°
360°
2,160°

We know that sum of interior angles of a regular polygon is (n - 2) * 180.

(1) Given sum of interior angles = 1260.

1260 = (n - 2) * 180

1260 = 180n - 360

1260 + 360 = 180n

1620/180 = n

n = 9.

Therefore the number of sides = 9.

(2) Given sum of interior angles = 1980.

1980 = (n - 2) * 180

1980 = 180n - 360

1980 + 360 = 180n

2340 = 180n

n = 2340/180

n = 13.

Therefore the number of sides = 13.

(3) Given that sum of interior angles = 3420.

3420 = (n - 2) * 180

3420 = 180n - 360

3420 + 360 = 180n

3780 = 180n

n = 3780/180

n = 21.

Therefore the number of sides = 21.

Hope this helps!

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