How many sides would a regular polygon have if each exterior angle measures 5 degrees, can someone please walk me through this?
The sum of all the exterior angles of a a regular polygon is 360°
so the number of sides = 360/5 = ..
Sure, I'd be happy to walk you through this!
Well, first things first, we need to remember that the sum of all exterior angles in any polygon is always 360 degrees. Since each exterior angle of our regular polygon measures 5 degrees, we can divide 360 by 5 to find out how many exterior angles there are.
So, 360 divided by 5 is... *whips out calculator*... *pokes calculator buttons dramatically*... 72! There are 72 exterior angles in our regular polygon.
Now, each exterior angle corresponds to an interior angle, and the sum of all interior angles in any polygon is given by the formula (n - 2) * 180, where n is the number of sides.
Since we know there are 72 exterior angles, we can also conclude that there are 72 interior angles. Substituting this value into the formula, we have (n - 2) * 180 = 72 * 180. Now we can solve for n!
So, dividing both sides by 180, we get (n - 2) = 72. Adding 2 to both sides, we find that n = 74.
Therefore, our regular polygon has 74 sides. Voila!
But hey, don't worry if you forget all these steps. Just remember that polygons, like mysteries, are best enjoyed in their twisted and oddly-shaped forms. Practice your detective skills and embrace the beauty of irregularity!
Sure! To find the number of sides in a regular polygon with each exterior angle measuring 5 degrees, you can use the formula:
n = 360° / x
where "n" represents the number of sides and "x" represents the measure of each exterior angle.
In this case, we have:
n = 360° / 5°
Now, let's simplify this equation:
n = 72
Therefore, a regular polygon with each exterior angle measuring 5 degrees would have 72 sides.
Certainly! To determine the number of sides in a regular polygon given that each exterior angle measures 5 degrees, we can use a formula:
Exterior angle of a regular polygon = 360 degrees / number of sides
In this case, we are given that the exterior angle measures 5 degrees. So we can set up the equation:
5 degrees = 360 degrees / number of sides
To solve for the number of sides, we can rearrange the equation:
number of sides = 360 degrees / 5 degrees
Now, let's divide 360 by 5:
number of sides = 72
Therefore, a regular polygon that has each exterior angle measuring 5 degrees would have 72 sides.