Answer :
To find the sum of the interior angles of a polygon, you can use the formula:
Sum of interior angles = (n - 2) * 180 degrees
where n is the number of sides of the polygon.
Since each exterior angle is 30 degrees, the corresponding interior angle is 180 - 30 = 150 degrees.
Thus, the number of sides, n, can be found by dividing 360 degrees (the total degrees in a full circle) by the exterior angle, which gives:
n = 360 / 30 = 12
Now, plug this value of n into the formula:
Sum of interior angles = (12 - 2) * 180 = 10 * 180 = 1800 degrees
So, the sum of the interior angles of the polygon is 1800 degrees.
