A regular polygon with interior angles measuring 165 degrees each will have exterior angles measuring 15 degrees each, since each pair of interior/exterior angles forms a linear pair whose measures total 180 degrees. For any polygon, the sum of the exterior angles is 360 degrees. You can find how many sides, and therefore vertices, in the polygon by dividing 360 by 15. In this case, the polygon has 360/15 = 24 sides.
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To determine the number of sides of a polygon with an interior angle of 165 degrees, we can use the formula for the interior angles of a polygon: (n-2) * 180 degrees, where n is the number of sides. Setting this equal to the given interior angle of 165 degrees, we get (n-2) * 180 = 165. Solving for n, we find n = 9 sides. Therefore, the polygon has 9 sides.
Well, isn't that a happy little question! If a polygon has an interior angle of 165 degrees, we can use the formula: sum of interior angles = (n-2) * 180 degrees, where n is the number of sides. So, for an angle of 165 degrees, we get (n-2) * 180 = 165. Solving for n, we find that the polygon has 12 sides. Happy painting!
Oh, dude, that's an easy one. So, like, to find the number of sides in a polygon, you just use the formula (n-2) * 180 = total interior angles. In this case, you have 165 degrees for each interior angle, so you just plug that in and solve for "n." So, like, the polygon has 11 sides. Easy peasy, right?
If each interior angle is 175 degrees then the polygon will have 72 sides
If it's a regular polygon and each interior angle is 176 degrees then it will have 90 sides
Exterior angle = 360/120 = 3 degrees. So interior angle = 180-3 = 177 degrees.
The sum of the EXTERIOR angles of a polygon is 360 degrees. The sum of the INTERIOR angles of a polygon with n sides is (n-2)*180 degrees. If it is a regular polygon, each interior angle is (n-2)/n*180 degrees.
If the interior angle = 140 degrees, then the exterior angle = 180 degrees - 140 degrees = 40 degrees. So the number of sides is 360 degrees / 40 degrees = 9 sides (a nonagon).