In a figure, 60° is the smallest angle of symmetry. What are the other angles of symmetry of this figure?
Step 1: Identify the smallest angle of symmetry = 60°
Step 2: Find all multiples of 60° that are less than or equal to 360°
60° × 1 = 60° 60° × 2 = 120° 60° × 3 = 180° 60° × 4 = 240° 60° × 5 = 300° 60° × 6 = 360°
Answer: The angles of symmetry are: 60°, 120°, 180°, 240°, 300°, and 360° This figure has 6 angles of symmetry and rotational symmetry of order 6.
Explanation
The chapter states that 'the angles are the multiples of the smallest angle.' If the smallest angle of symmetry is 60°, then all multiples of 60° (60°, 120°, 180°, 240°, 300°, 360°) are angles of symmetry.
Solution Steps
Step 1: Identify the smallest angle of symmetry = 60°
Step 2: Find all multiples of 60° that are less than or equal to 360°
Step 3: 60° × 1 = 60°
Step 4: 60° × 2 = 120°
Step 5: 60° × 3 = 180°
Step 6: 60° × 4 = 240°
Step 7: 60° × 5 = 300°
Step 8: 60° × 6 = 360°
Step 9: The angles of symmetry are: 60°, 120°, 180°, 240°, 300°, 360°