Three exterior angles of a polygon are 30\(^o\), 40\(^o\) and 60\(^o\). If the remaining exterior angles are 46\(^o\) each, name the polygon.

Assessment: WAEC SSCE - General Mathematics - 2017 (Objective) Subject: General Mathematics

Question 1 Report

Three exterior angles of a polygon are 30\(^o\), 40\(^o\) and 60\(^o\). If the remaining exterior angles are 46\(^o\) each, name the polygon.

Answer Details
The sum of all exterior angles of a polygon is 360 degrees. Exterior angles are formed by extending one side of a polygon to the next. So, the sum of the three exterior angles that we know is 30 + 40 + 60 = 130 degrees. And, if each of the remaining exterior angles measures 46 degrees, then there must be 360 - 130 = 230 degrees left. Dividing this by 46, we get 230/46 = 5. So, the polygon has a total of 5 + 3 = 8 sides. Therefore, the polygon is an octagon.

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