Each of the interior angles of a regular polygon is 140o. How many sides has the polygon?

Assessment: JAMB UTME - Mathematics - 2012 Subject: General Mathematics

Question 1 Report

Each of the interior angles of a regular polygon is 140o. How many sides has the polygon?
Answer Details
For a regular polygon with n sides, each interior angle is given by: interior angle = (n-2) x 180 / n We are given that each interior angle of the polygon is 140 degrees. Substituting this into the formula, we get: 140 = (n-2) x 180 / n Multiplying both sides by n, we get: 140n = (n-2) x 180 Expanding the right-hand side, we get: 140n = 180n - 360 Simplifying and isolating n, we get: n = 360 / (180 - 140) n = 360 / 40 n = 9 Therefore, the regular polygon has 9 sides. Hence, the answer to the question is 9.
Read lesson note on Triangles And Polygons (WAEC)
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