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Suppose there are N sides to this polygon. Draw a line from each corner to a point inside the polygon. That makes N triangles. The total of all the angles must be Nx180 degrees. But that includes 360 degrees around the point. Take that away and you have all the angles adding up to (N-2)x180 degrees. If you want this to be 720 (which is 180x4) then (N-2)x180 equals 4x180, so N-2=4 so N=6. So only a 6 sided polygon makes 720 degrees.
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What is the total degree of all angles and individual angle measurement of your regular polygon?
The sum of all the internal angles of a polygon with n sides is 180*(n-2) degrees. In a regula polygon, therefore, each internal angle is 180*(n-2)/n degrees. Also The sum of all the external angles in 360 degrees. The sum of each external angle in a regular polygon is 360/n degrees.
If each interior angle of an equiangular polygon is a 144 degree angle how many sides does this polygon have?
Since the amount of sides of a polygon is equal to the amount of angles, we have:144x = total anglesThe total measure of each angle is determined by 180(x - 2), by splitting it into several triangles. Thus:144x = 180(x - 2)144x = 180x - 360360 = 36xx = 10This polygon has 10 sides (a decagon).
Can a regular polygon have interior angle of 30 degrees?
the formula for the total number of degrees in a polygon is (x=number of sides) (x-2)180=total degree measure and you divide that number by x to get each angle measure of a regular polygon. so ((x-2)180)/x=30 solve for x and you get x=2.4 you can't have 2.4 sides in a polygon. so no, a regular polygon can't have an interior angle of 30 degrees
Angle of refraction is less than 90 degree true or false?
False. You can have total internal reflection where the effective angle is greater than 90 deg
What is the angle between two adjacent sides of a 12 sided regular polygon?
Any polygon has a total external angle of 360 degrees This is split between all the angles around the shape, n the case of a regular polygon they would also be equal, so the external angles would be 360 / 12, which is 30. However you need to know the internal angles As you know there are 180 degrees in a straight line, the external angle is 30 degrees as explained above, so the internal angle is 180 - 30, which is 150 degrees
