I need help with this question

The sum of the  interior and exterior angles = 180°

So......this means that

x +  29x = 180

30x  =  180

x =  6°

And the measure of any exterior angle   is given by

360 / N      where N is the number of sides  ..so....

360 / N  =  6      multiply both sides by  N   

360 =  6N       divide both sides by 6

60  = N  = the number of sides

Proof  ....  this "formula"  gives the measire of an interior angle of a regular polygon of N sides

(N - 2) * 180 / N

When N  = 60, we have

(60 - 2) 180 / 60   =   58 * 3  =   174°

So...... 174°  + 6°   =  180°

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. 

Good...!!!!...two great minds can't possibly be incorrect....can they   ???

LOL!!!!

BTW - I liked that tecnique you used on that  parabola - focus - directrix problem yesterday

I added that one  to  my "tool chest"