Qstnid -B-7- The Exterior Angle Of A Regular Polygon Is One-third Of Its Interior Angle. Find The Number Of Sides In The Polygon. - 16: Understanding Shapes (Including Polygons) Class 8 Maths - Icse-viii-mathematics

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ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

with Solutions - page 4

Qstn# B-7 Prvs-Qstn Next-Qstn

#7
The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides in the polygon.
Ans : Let interior angle = x°
Exterior angle = 1/3 x°

∴ x + 1/3x = 180˚
⇒ 3x + x = 540
⇒ 4x = 540
⇒ x = 540/4
⇒ x = 135˚
∴ Exterior angle = 1/3 × 135˚ = 45˚
Let no. of sides = n
∵ Each exterior angle = 360˚/n
∴ 45˚ = 360˚/n
∴ n = 360˚/45˚
⇒ n = 8