"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**+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

#2**+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