Consider the following statements 1 If n 3 and m 3 are distinct positive integers then the sum of th...........

Quantitative Aptitude (CDS) Coordinate Geometry

Consider the following statements

1. If n $\geq$ 3 and m $\geq$ 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 $\geq$ 3.Then, the sum of the interior angles of a regular polygon ofmsides is greater than the sum of the interior angles of a regular polygon of n sides and their sum is $(m+n)\frac{ \pi }{2}$

Which of the following statement(s) is correct?

Only 1

Only 2

Both 1 and 2

Neither 1 nor 2

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Explanation:

1. In regular ploygon, Sum of exterior angles = 360° [which is always constant]
So, Statement 1 is incorrect.
2. Sum of interior angles of m sides = (m− 2) × 180° of regular polygon
Total sum of interior angles ofmsides and n sides of regular polygon = (m− 2) × 180°+ (n − 2) × 180° = (m+ n − 4) × 180°
So, Statement 2 is incorrect.
Hence, neither 1 nor 2 is correct.