#1**0 **

1. At the vertex of a polygon, the sum of the exterior angle and the interior angle is 180^{o}.

Since the interior angle is 12 times the exterior angle, the exterior angle has to be 15^{o}.

The sum of all exterior angles of a polygon is 360^{o}, irrespective of the number of sides.

Therefore, the polygon has 360 / 15 = 24 vertices.

We shall presuppose that a polygon has the same number of sides as it has vertices,

Therefore, this polygon has **24 sides**.

_{.}

Bosco Apr 26, 2024