If each interior angle of a regular polygon is $1\dfrac{1}{3}$ right angle. The number of sides in the polygon is:

1. 4

2. 5

3. 6

4. 8

It is given that each interior angle of a regular polygon is $1\dfrac{1}{3}$ right angles.

Interior angle = $1\dfrac{1}{3} \times 90°$

= $\dfrac{4}{3} \times 90°$

= $\dfrac{360°}{3}$

= 120°

According to the properties of a polygon, if a polygon has n sides, each of its interior angles is $\dfrac{(2n - 4) 90°}{n}$.

⇒ $\dfrac{(2n - 4) 90°}{n}$ = 120°

By cross multiplying, we get

⇒ (2n - 4) x 90° = 120°n

⇒ 180°n - 360° = 120°n

⇒ 180°n - 120°n = 360°

⇒ 60°n = 360°

⇒ n = $\dfrac{360°}{60°}$

⇒ n = 6

Hence, option 3 is the correct option.