If the ratio of an external angle and an internal angle of a regular polygon is 1 5 then what is the...........

Quantitative Aptitude (MTS) Ratio, Proportion

If the ratio of an external angle and an internal angle of a regular polygon is 1 : 5 , then what is the number of sides in the

polygon?

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SSC MTS 22nd July 2022 Shift-2

- External Angle: In a regular polygon, each external angle is given by 360°/n, where n is the number of sides.

- Internal Angle: Each internal angle of a regular polygon is (n-2) * 180°/n.

- Ratio Given: The ratio of an external angle to an internal angle is given as 1:5.

- Equation Setup: 360°/n : [(n-2)*180°/n] = 1:5.

- Solve the Equation: This implies 360/(n-2) * 180 = 1/5. Simplify to get n = 12.

- Option Analysis:

- Option 1: 24 sides do not fit the condition.

- Option 2: 22 sides do not fit the condition.

- Option 3: 12 sides correctly fit the condition.

- Option 4: 30 sides do not fit the condition.

- Answer: Option 3 - 12

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