Question

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

Answer 1

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.