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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?

watchdoge  Oct 25, 2017
 #1
avatar+91116 
+3

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°

 

 

cool cool cool

CPhill  Oct 25, 2017
 #3
avatar+349 
+2

Wow, we have the same method xD

Mathhemathh  Oct 25, 2017
 #7
avatar+8 
+1

Thanks!​

smileysmiley

watchdoge  Oct 26, 2017
 #2
avatar+349 
+2

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. wink

Mathhemathh  Oct 25, 2017
 #4
avatar+91116 
+1

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"

 

 

cool cool cool

CPhill  Oct 25, 2017
 #5
avatar+349 
+2

Thanks laugh

Mathhemathh  Oct 25, 2017

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