If a polygon has 33 sides what is
a) The sum of the measures of the angles of the polygon?
b) The sum of the measures of the exterior angles, one per vertex, of the polygon?
33-2(180)
31*180
5580
tfttft
a) Well, let's bring in the "Triangle Gang" to help us out! A triangle has 3 sides and the sum of its angles is 180 degrees. So, if we have a 33-sided polygon, we can divide it into 33 triangles. Each triangle has 180 degrees, so the sum of the angles of the polygon is 33 times 180. That's a whopping 5,940 degrees! Talk about getting into shape!
b) Ah, the exterior angles, the hipsters of the polygon world! To find the measure of each exterior angle, we can use a little trick. The sum of the exterior angles of any polygon is always 360 degrees. So, we divide that by 33, and voila! Each exterior angle in your 33-sided polygon measures approximately 10.91 degrees. That's a pretty chill and trendy polygon, if you ask me!
To find the sum of the measures of the angles of a polygon with 33 sides, we can use the formula:
a) The sum of the measures of the angles of a polygon with n sides is given by the formula: (n-2) * 180 degrees.
So, for a polygon with 33 sides, the sum of the measures of the angles would be:
(33 - 2) * 180 = 31 * 180 = 5580 degrees.
b) The sum of the measures of the exterior angles of any polygon is always 360 degrees. This is because if you add up all the exterior angles of a polygon as you move around its vertices, you will complete a full circle.
So, for a polygon with 33 sides, the sum of the measures of the exterior angles would be:
360 degrees.