A shape has three sides if its interior angles add up to equal 180 degrees.
36 sides
Since each interior angle is 150 degrees, each exterior angle is 180-150 = 30 degrees. Therefore, the polygon has 360/30 = 12 sides.
Divide the number of sides into 360 degrees and then subtract your answer from 180 degrees to give you the interior angle. For example a regular hexagon has 6 equal sides and 360 divided by 6 = 60 degrees (the exterior angle) 180 - 60 = 120 degrees (the interior angle)
If interior angle is 178o then the exterior angle = 180 - 178 = 2o So the number of sides = 360 / 2 = 180 sides.
To work out the angle of any 'perfect shape' you use this formula: interior angle =((number of sides - 2) x 180)/ number of sides for an octagon: interior angle =((8-2) x 180 )/ 8 = 135 degrees
If one interior angle is 165 degrees, find the number of sides of the polygon.
If it is a regular polygon and each interior angle is 176 degrees then it will have 90 sides.
interior angle = (number of sides - 2) * 180 / (number of sides) = 4 * 180 / 6 = 120 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).
36 sides
If each interior angle is 178 degrees then the regular polygon will have 180 sides.
Smallest possible interior angle of regular polygon is 60 degrees (triangle). The greater the number of sides, the greater each interior angle. If exterior angle is 30 degrees, the polygon has 12 sides.
Interior angle = 174 so exterior angle = 180-174 = 6 degrees. Therefore, number of sides = 360/exterior angle = 360/6 = 60 sides.
Since each interior angle is 150 degrees, each exterior angle is 180-150 = 30 degrees. Therefore, the polygon has 360/30 = 12 sides.
Divide the number of sides into 360 degrees and then subtract your answer from 180 degrees to give you the interior angle. For example a regular hexagon has 6 equal sides and 360 divided by 6 = 60 degrees (the exterior angle) 180 - 60 = 120 degrees (the interior angle)
If it's a regular polygon and each interior angle is 176 degrees then it will have 90 sides
If interior angle is 178o then the exterior angle = 180 - 178 = 2o So the number of sides = 360 / 2 = 180 sides.