A graphics designer wants to use a star-shaped polygon
with 10 points and a point angle of 12 degrees. What should be
the dent angle of this polygon?
if you are traveling along the leg of the star, the deflection angle is the angle you have to turn to get to the next leg.
d = deflection angle at a point
= 180 - 12 = 168
since there are points, the total point deflection angle at the points is 1680.
x = dent angle = 180+y
y = deflection angle at dent
To end where you start, you must have a total deflection of 360 degrees so,
360 = 1680 + 10y
reducing this,
y = -132
so x = 48 degrees
To find the dent angle of a polygon, we need to know the total angle around each vertex. In this case, we have a star-shaped polygon with 10 points and a point angle of 12 degrees.
To calculate the total angle around each vertex, we subtract the point angle from 180 degrees (since the sum of interior angles of any polygon is 180 degrees).
So, the total angle around each vertex would be 180 - 12 = 168 degrees.
Since this polygon has 10 points, it means that there are 10 vertices. To find the dent angle, we divide the total angle around each vertex by the number of points:
Dent angle = (Total angle around each vertex) / (Number of points)
= 168 / 10
= 16.8 degrees
Therefore, the dent angle of this polygon should be 16.8 degrees.