Each corner of a polygon is 135 degrees, how many sides does it have?

By condition, each angle of the polygon is 135 degrees, which means this polygon is regular (that is, all its angles and sides are equal). You need to find the number of sides, for this we use the formula to find the angle in a regular n-gon: a (angle) = (n-2) * 180 degrees / n; where n is the number of sides of the polygon. Substitute the known angle value and find n. 135 = (n-2) * 180 / n Multiply both sides of the equality by n to get rid of the denominator.
135n = (n-2) * 180
135n = 180 n – 360, move 180n to the left side of the equation
135n – 180n = – 360
-45n = – 360
n = 8.
This means that a regular polygon with an angle of 135 degrees has 8 sides.
Answer 8.