In a regular polygon, the size of an interior angle interior angle is 20° more than thrice times the size of its exterior angle. Find the number of the sides of this polygon
Let x be the size of the exterior angle.
According to the given information, the size of the interior angle is 20° more than thrice the size of the exterior angle. Therefore, the size of the interior angle can be expressed as 3x + 20.
Since the sum of the interior and exterior angles of a polygon is 180°, we can write the following equation:
3x + 20 + x = 180
Combining like terms:
4x + 20 = 180
4x = 160
x = 40
Therefore, the exterior angle of the polygon is 40°.
The number of sides in a regular polygon can be found using the formula:
Number of sides = 360° / Exterior angle
Number of sides = 360 / 40 = 9
Therefore, the polygon has 9 sides.