Mathematics 2014 JAMB Past Questions - Question 25: How many sides has a regular polygon whose interior angle is 135° each ?

Correct Answer

A

Explanation

If each interior angle of the polygon is 135,, then each exterior angle is 180 - 135 = 45 hence,number of sides= 360 / one exterior angle= 360 / 45To determine the number of sides in a regular polygon with interior angles measuring 135 degrees each, we can use the formula:Interior angle = (n - 2) * 180 / nwhere n represents the number of sides of the polygon.Given that the interior angle is 135 degrees, we can substitute this value into the formula:135 = (n - 2) * 180 / nTo simplify the equation, we can multiply both sides by n:135n = 180(n - 2)Expanding the equation, we get:135n = 180n - 360Now, let's isolate the variable n by moving all the terms involving n to one side of the equation:180n - 135n = 36045n = 360Dividing both sides of the equation by 45, we find:n = 8Therefore, a regular polygon with interior angles measuring 135 degrees each has 8 sides.= 8