Assertion (A) : The ratio between the exterior and interior angle of a regular polygon is 1 : 8. The number of sides of the regular polygon is 18.

Reason (R) : The sum of the exterior angle and interior angles of a convex polygon are 360° and 2(n - 1) x 90° respectively.

1. Both A and R are correct, and R is the correct explanation for A.

2. Both A and R are correct, and R is not the correct explanation for A.

3. A is true, but R is false.

4. A is false, but R is true.

Let each interior angle be I and exterior angle be E.

Given, the ratio between the exterior and interior angle of a regular polygon is 1 : 8.

$\Rightarrow \dfrac{E}{I} = \dfrac{1}{8}$

⇒ I = 8E

For any polygon, the exterior and interior angles at each vertex are supplementary,

⇒ I + E = 180°

⇒ 8E + E = 180°

⇒ 9E = 180°

⇒ E = $\dfrac{180°}{9}$ = 20°

⇒ I = 8E = 8 x 20° = 160°

The exterior angle E of a regular polygon with n sides is given by :

⇒ E = $\dfrac{360°}{n}$

⇒ 20° = $\dfrac{360°}{n}$

⇒ n = $\dfrac{360°}{20°}$

⇒ n = 18.

So, assertion (A) is true.

We know that,

The sum of exterior angles = 360°.

The sum of interior angles = (n - 2) x 180° = 2(n - 2) x 90°.

So, reason (R) is false.

∴ A is true, but R is false.

Hence, option 3 is the correct option.