The number of sides of two regular polygons are in the ratio 5 : 4. The difference between their interior angles is 9°. Consider the following statements: 1) One of them is pentagon and the other is a rectangle. 2) One of them is decagon and the other is an octagon. 3) The sum of their exterior angles is 720°. Which of the above statements is/are correct?

1 only
2 only
1 and 3
2 and 3

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 4 : 2 and 3

Let the number of sides of the two polygons be ‘5x’ and ‘4x’

∵ Measure of interior angle of regular polygon with ‘n’ sides = (n - 2) × 180°/n

Given, difference between interior angles = 9°

⇒ - = 9°

⇒ - = 9°

⇒ x180° - 72° - x180° + 90° = x9°

⇒ 18° = x9°

⇒ x = 2

⇒ One of them is a decagon (10 sides) and other is an octagon (8 sides)

Now,

Sum of exterior angles of a regular polygon = 360°

⇒ Sum of exterior angles of the two polygons = 360° + 360° = 720°

∴ Statements 2 and 3 are correct.

4 views Answered 2022-09-04 04:29

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