Since the interior angle is 29x, and the exterior angle is x, then \(29x+x=180\).
Combine like terms: \(30x=180\)
Divide both sides by 30: \(x=6\).
Now, the exterior angle measures 6˚. We know that the sum of all exterior angles add up to 360˚. So... \(6s=360\), where s is the number of sides.
Divide both sides by 6: \(s=60\).
The polygon has 60 sides.