Math Problem Statement

What is the Angle of Rotation?

Solution

The image shows a regular polygon, specifically an octagon (8-sided figure), with the question "What is the angle of rotation?".

For regular polygons, the angle of rotation can be calculated using the formula:

Angle of rotation=360n\text{Angle of rotation} = \frac{360^\circ}{n}

where nn is the number of sides of the polygon.

Since this is an octagon (n=8n = 8):

Angle of rotation=3608=45\text{Angle of rotation} = \frac{360^\circ}{8} = 45^\circ

Therefore, the correct answer is 45°.

Would you like any more details or further clarification?

Here are 5 related questions:

  1. How would the angle of rotation change for a decagon (10-sided polygon)?
  2. What is the total sum of the interior angles of an octagon?
  3. How does rotational symmetry relate to the angle of rotation?
  4. Can irregular polygons have rotational symmetry?
  5. What is the difference between rotational and reflectional symmetry?

Tip: The smaller the number of sides, the larger the angle of rotation for a regular polygon.

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Math Problem Analysis

Mathematical Concepts

Geometry
Symmetry
Rotational Symmetry

Formulas

Angle of Rotation = 360° / n

Theorems

Rotational Symmetry Theorem

Suitable Grade Level

Grades 7-9