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I need help with this question

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"The exterior angle of regular polygon A is \(x°\)
The interior angle of regular polygon A is \(29x°\)
Find the number of sides regular polygon A has"

How would you solve this question?

Oct 25, 2017

#1
+95859
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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°

Oct 25, 2017
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Wow, we have the same method xD

Mathhemathh  Oct 25, 2017
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Thanks!​

watchdoge  Oct 26, 2017
#2
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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.

Oct 25, 2017
#4
+95859
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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"

Oct 25, 2017
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Thanks

Mathhemathh  Oct 25, 2017