Let's analyze and solve the questions in the uploaded image:

(a) If the sides of a polygon are produced in order, the sum of the exterior angles so formed is:

• Key Concept: For any polygon (regular or irregular), the sum of the exterior angles, taken one at each vertex, is always 360°.
• Correct Option: (ii) 360°

(b) In a regular polygon, each interior angle is twice the exterior angle. The number of sides of the polygon is:

• Key Concept:

  1. Exterior angle of a regular polygon = $\frac{360^\circ}{n}$, where $n$ is the number of sides.
  2. Interior angle = $180^\circ - \text{Exterior angle}$.
  3. According to the question, Interior angle = 2 × Exterior angle: $180^\circ - \frac{360^\circ}{n} = 2 \times \frac{360^\circ}{n}.$

• Solution: Simplify the equation: $180^\circ = 3 \times \frac{360^\circ}{n}.$ Rearrange for $n$: $n = \frac{3 \times 360^\circ}{180^\circ} = 6.$

• Correct Option: (i) 6

Final Answers:

(a) (ii) 360°
(b) (i) 6

Would you like a detailed breakdown or further explanation of the steps?

Here are 5 related questions to expand your understanding:

1. What is the formula to calculate the sum of interior angles of a polygon?
2. Why is the sum of exterior angles always 360°, regardless of the number of sides?
3. What is the relationship between the interior and exterior angles of a polygon?
4. How do you calculate the number of sides of a polygon if the exterior angle is known?
5. What is the difference between a regular polygon and an irregular polygon?

Tip: Remember that the sum of exterior angles of any polygon is always 360°, a helpful rule for quick calculations!