In a polygon the interior and exterior angles at each vertex are 5:1 how many sides does it have
You must mean a regular polygon such that
interior : exterior = 1 : 5, (not 5:1, the interior angle cannot be greater than the exterior to make a polygon)
let the two angles be x and 5x
x + 5x = 360
x = 60
so it must be an equilateral triangle, each angle is 60°
(If it is not a regular polygon, then you did not give enough information)
eh? Seems to me that at each vertex the interior and exterior angles sum to 180.
So, interior is 150, exterior is 30.
If the interior angles are 150, then we need to find an n such that
n*150 = (n-2)*180
30n = 360
n = 12
So, a dodecagon has interior angles of 150 and exterior angles of 30.
Steve, I was looking at it as a complete rotation of 360° , which explains my first sentence.
So, yay - the student can take his pick.
Is there a difference between interior/exterior and internal/external angles?
To determine the number of sides in a polygon with a given ratio of interior and exterior angles, we need to use the formula:
180 * (n - 2) / n
Where 'n' represents the number of sides in the polygon.
In this case, the ratio of interior and exterior angles is 5:1. This means that for every 5° increase in the interior angle, the exterior angle increases by 1°.
Let's assume that the interior angle measures 5x, and the exterior angle measures x. Then we can calculate the ratio:
5x / x = 5 / 1
This simplifies to:
5x = 5
Now, we can solve for x by dividing both sides of the equation by 5:
x = 1
So, the exterior angle measures 1° and the interior angle measures 5x = 5°.
Now, let's substitute this value into the formula:
180 * (n - 2) / n = 5
Multiplying both sides by 'n' to eliminate the denominator:
180 * (n - 2) = 5n
Expanding the equation:
180n - 360 = 5n
Combining like terms:
180n - 5n = 360
175n = 360
Dividing both sides by 175:
n = 360 / 175
Using a calculator, we find that n is approximately 2.06. However, since n represents the number of sides in a polygon, it must be a whole number. Therefore, we round up to the nearest whole number.
Thus, the polygon has 3 sides.