Q1 of 15 Page 134

In a regular polygon, the ratio of the ratio of the inner and outer angle is 7 : 2. What is each angle? How many sides does the polygon have?

Ratio of the inner and outer angle = 7 ∶ 2

Let, inner angle = 7x and outer angle = 2x


According to problem,


⇒ 7x + 2x = 180°


⇒ 9x = 180°


⇒ x = 180°/9


⇒ x = 20°


∴ Inner angle = 7x = 7 × 20° = 140°


Outer angle = 2x = 2 × 20° = 40°


∴ No. of sides of the polygon,


⇒ 360°/outer angle


⇒ 360°/40°


⇒ 9


∴ The polygon have 9 sides.


More from this chapter

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2

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There are four right triangles, the ratio of perpendicular sides being 3 : 4 in each. Once more fact about each is given below. Find the lengths of the sides of each triangle.

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