A multiple choice answers for the question. What is the measure of the dent angle for a star-shaped polygon with 20 points and a dent angle of 12 degrees?
Asnwers are; 30 degrees, 50 degrees, 60 degrees, 90 degrees. How do I find the answer?
The angle at the tip of the star's points is called the point angle, and the angle subtended by two adjacent sides between two points is the dent angle.
In this case, the point angle, p, is 12° and there are 20 points (=n) in the star.
The dent angle can be obtained by:
D=(360/n)+p
=(360/20)+12
= 30 °.
To find the measure of the dent angle for a star-shaped polygon with 20 points, you can use the formula:
Dent Angle = 360° / Number of Points
In this case, the number of points is 20. Substituting this value into the formula:
Dent Angle = 360° / 20 = 18°
Since the given dent angle is 12 degrees, we can see that it is less than the calculated dent angle of 18 degrees. Therefore, none of the provided options (30 degrees, 50 degrees, 60 degrees, 90 degrees) matches the correct answer.