The problem states that the size of each interior angle of a regular polygon is $135^\circ$. We need to find the number of sides of the polygon and the order of rotational symmetry of the polygon.
2025/6/9
1. Problem Description
The problem states that the size of each interior angle of a regular polygon is . We need to find the number of sides of the polygon and the order of rotational symmetry of the polygon.
2. Solution Steps
(a) Find the number of sides of the polygon.
First, we find the exterior angle of the polygon. The exterior angle and interior angle are supplementary, meaning they add up to .
The sum of exterior angles of any polygon is . For a regular polygon with sides, each exterior angle is .
So, we have:
Therefore, the number of sides of the polygon is
8.
(b) State the order of rotational symmetry of the regular polygon.
For a regular polygon, the order of rotational symmetry is equal to the number of sides.
Since the polygon has 8 sides, the order of rotational symmetry is
8.
3. Final Answer
(a) The number of sides of the polygon is