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Consider the following statements: 1. There exists a regular polygon whose exterior angle is 70°. 2. Let n ≥ 5. Then the exterior angle of any regular polygons of n sides is acute. Which of the above statements is/are correct?

Consider the following statements: 1. There exists a regular polygon whose exterior angle is 70°. 2. Let n ≥ 5. Then the exterior angle of any regular polygons of n sides is acute. Which of the above statements is/are correct? Correct Answer 2 only

Exterior angle of a n sides regular polygon = 360/n

Statement I:

360/n = 70°

There exists no natural number n for which 360/n = 70°

⇒ Statement I is false

Statement II:

If n ≥ 5, Exterior angle ≤ 360/5

⇒ Exterior angle ≤ 72

⇒ Exterior angle is acute

⇒ Statement II is true

∴ Only statement II is true.

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