Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.

It is given that the interior angle is equal to the exterior angle.

Let the exterior angle be a. Therefore, the interior angle is also a.

We know that the sum of an interior angle and its corresponding exterior angle is 180°,

⇒ a + a = 180°

⇒ 2a = 180°

⇒ a = $\dfrac{180°}{2}$

⇒ a = 90°

Thus, both the interior angle and the exterior angle are 90°.

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

⇒ $\dfrac{(2n - 4) \times 90°}{n}$ = 90°

By cross-multiplying, we get

⇒ (2n - 4) x 90° = 90°n

⇒ 180°n - 360° = 90°n

⇒ 180°n - 90°n = 360°

⇒ 90°n = 360°

⇒ n = $\dfrac{360°}{90°}$

⇒ n = 4

Hence, the number of sides is 4.