The sum of the interior and exterior angles at the same vertex is always 180 degrees or 1 straight angle. So, if there are 1000 st angles, then there must be 1000 vertices and so 1000 sides.
The sum of the interior angles is found by: (number of sides-2)*180 degrees Exterior angles add up to 360 degrees Angles on a straight line add up to 180 degrees
No because an exterior angle and an interior angle of a polygon add up to 180 degrees but exterior angles around a polygon add up to 360 degrees
The exterior angles of any polygon add up to 360 degees so if it's a regular polygon each exterior angle is 360/number of sides. Or 180 -interior angle = exterior angle because angles on a straight line add up to 180 degrees.
A rectangle (or square).
Such a polygon does not exist because the interior angle of any polygon can't be greater than 180 degrees Each interior and exterior angles of any polygon add up to 180 degrees because there are 180 degrees on a straight line
The exterior and interior angles of each vertex of a polygon add up to 180 degrees.
18 Angles on a straight line = 180 degrees interior angles 2880 + exterior angles 360 = 3240 degrees 3240 divided by 180 = 18 sides Note that the exterior sum of angles of any polygon is always 360 degrees.
A Regular Polygon
octagon interior=135 exterior=45
The sum of the interior angles is found by: (number of sides-2)*180 degrees Exterior angles add up to 360 degrees Angles on a straight line add up to 180 degrees
The sum of each pair of interior and exterior angles of a polygon is always 180 degrees.
The easiest way to solve this is to use the exterior angles of the polygon. The sum of an exterior angle and interior angle is 180o. Also the sum of all the exterior angles of a polygon is 360o. As the polygon is regular, all the interior angles are the same and all the exterior angles are the same. So, for an interior angle of 172o the exterior angle is 180-172 = 8o. The sum of all the exterior angles is 360o so how many 8o make up 360o? 360/8=45. Thus the polygon with interior angles of 172o has 45 sides.
If you multiply 360 by the number of angles in the polygon and then subtract the sum of all the interior angles you will end up with the sum of all the exterior angles of the polygon.
No because an exterior angle and an interior angle of a polygon add up to 180 degrees but exterior angles around a polygon add up to 360 degrees
The exterior angles of any polygon add up to 360 degees so if it's a regular polygon each exterior angle is 360/number of sides. Or 180 -interior angle = exterior angle because angles on a straight line add up to 180 degrees.
An equilateral triangle.
In a polygon there are no such angles.