Suppose you have a polygon with n sides, the measure of each interior angle is given by the equation [180(n-2)]/n. We can prove this expression with a regular triangle. We know that the triangle has 3 sides. Plugging this into our expression gives us: [180(1)]/3=60 degrees per angle, which is the standard value of an angle for a triangle.
Now, your situation is the opposite of what we have shown above. You have the measure of each angle, but not the number of sides. We can find an equation for the number of sides of a polygon by manipulating the expression mentioned above algebraically. Assume that the measure of each interior angle is given by the variable x. :
Original equation: [180(n-2)]/n=x.
Multiply each side by n: 180(n-2)=xn
Expand the left side: 180n-360=xn
Move the terms around: 180n-xn=360
Simplify: n(180-x)=360
Final expression: n=360/(180-x)
To better illustrate this, I will provide an example. Let's say you have a regular hexagon. You are given that each interior angle is 120.
Plugging this into the expression for number of sides: n=360/(180-120)
We have n=6, which is indeed the number of sides a hexagon has.
Hint: in a regular polygon interior plus exterior = 180o, always.
If it is a regular polygon and each interior angle measures 156 degrees then it will have 15 sides
Each interior angle measures 140 degrees
There is no regular polygon with an interior angle of 20o. If the interior angle is 120o then there are six sides and the sum of the angles is 720o.
540 degrees
Hint: in a regular polygon interior plus exterior = 180o, always.
1260
hexagon
The interior angle of any regular polygon can be calculated using the formula 180 * (n - 2) / n, where n is the number of sides. In this case, since each exterior angle measures 72 degrees, the interior angle would be 180 - 72 = 108 degrees. So the measures of the interior angles in this regular polygon would be 108 degrees.
1440 degrees
1440 degrees
The polygon will have 12 equal sides and each interior angle measures 150 degrees.
15
It is a regular 20 sided polygon
A four-sided regular polygon (square or rectangle) has 900 interior angles.
360
If it's a regular polygon then each interior angle measures 120 degrees.