What is the measure of the dent angle for a star-shaped polygon with 20 points and a dent angle of 12 degrees?

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This has multiple choice answers; 30 degrees, 50 degrees, 60 degrees, 90 degrees? What is the answer?

To find the measure of the dent angle for a star-shaped polygon, you need to know two things: the number of points in the star-shaped polygon and the total interior angle of the polygon.

The formula to calculate the total interior angle of a star-shaped polygon is:

Total Interior Angle = (n - 2) * 180,

where n represents the number of points in the polygon.

In this case, you have 20 points, so let's substitute that into the formula:

Total Interior Angle = (20 - 2) * 180
= 18 * 180
= 3240 degrees.

Now, you know that the total interior angle is 3240 degrees. A star-shaped polygon consists of multiple dent angles, and since the question specifies the dent angle as 12 degrees, we need to divide the total interior angle by the number of dent angles.

Number of Dent Angles = Total Interior Angle / Dent Angle
= 3240 degrees / 12 degrees
= 270 dent angles.

Therefore, the measure of the dent angle for a star-shaped polygon with 20 points and a dent angle of 12 degrees is 12 degrees.