Final answer:
The polygon has 24 sides.
Step-by-step explanation:
A polygon is a closed figure made up of straight sides. The sum of the exterior angles of a polygon is always 360 degrees. Let's assume the number of sides of the polygon is 'n'.
Half of the exterior angles are 10 degrees, so the other half must be 20 degrees. So, if we have 'n' sides, 'n/2' exterior angles will be 10 degrees and 'n/2' exterior angles will be 20 degrees.
Using the property that the sum of all exterior angles of a polygon is 360 degrees, we can write the equation:
n/2 * 10 + n/2 * 20 = 360
Simplifying the equation, we get:
5n + 10n = 360
15n = 360
n = 24
Therefore, the polygon has 24 sides.