2016 · Q78
Consider the following statements :
- 1If n ≥ 3 and m ≥ 3 are distinct positive integers, then the sum of the exterior angles of a regular polygon of m sides is different from the sum of the exterior angles of a regular polygon of n sides.2. Let m, n be integers such that m > n ≥ 3. Then the sum of the interior angles of a regular polygon of m sides is greater than the sum of the interior angles of a regular polygon of n sides, and their sum is (m+n)π/2Which of the above statements is/are correct?
Elementary MathematicsQuadrilaterals and Polygons
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
The exterior-angle sum of any convex polygon is 360°, so statement 1 is false. The interior-angle sums are (m−2)π and (n−2)π, totalling (m+n−4)π, not (m+n)π/2, so statement 2 is false. Hence neither, option D.