+0

# I need help with this question

+1
134
7
+8

"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
Sort:

#1
+80931
+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°

CPhill  Oct 25, 2017
#3
+302
+2

Wow, we have the same method xD

Mathhemathh  Oct 25, 2017
#7
+8
+1

Thanks!​

watchdoge  Oct 26, 2017
#2
+302
+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.

Mathhemathh  Oct 25, 2017
#4
+80931
+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"

CPhill  Oct 25, 2017
#5
+302
+2

Thanks

Mathhemathh  Oct 25, 2017

### 11 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details