"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?
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.