Question 6 of 7advanced🔍 AnalyzeShort Answer3 marks

In a figure, 60° is an angle of symmetry. The figure has two angles of symmetry less than 60°. What is its smallest angle of symmetry?

Correct Answer

Given: 60° is an angle of symmetry. There are two angles of symmetry less than 60°.

Rule: All angles of symmetry are multiples of the smallest angle.

Step 1: Let the smallest angle of symmetry be x.

Step 2: The angles less than 60° must be x and 2x.

Step 3: So 3x = 60°

Step 4: x = 60° ÷ 3 = 20°

Answer: The smallest angle of symmetry is 20°.

Exercise: Figure it Out (Section 4) | Q: 5 | (Page Page 22)
For More Understanding

Explanation

The chapter explains that angles of symmetry are multiples of the smallest angle. If 60° is an angle of symmetry and there are two angles smaller than 60°, those must be 20° and 40° (multiples of 20°). This means the smallest angle is 20°.

Solution Steps

  1. Step 1: 60° is an angle of symmetry

  2. Step 2: There are two angles of symmetry less than 60°

  3. Step 3: All angles of symmetry are multiples of the smallest angle

  4. Step 4: Let the smallest angle be x

  5. Step 5: The angles less than 60° must be x and 2x

  6. Step 6: So 3x = 60°, giving x = 20°

  7. Step 7: The smallest angle of symmetry is 20°

PreviousNext