Qstnid -B-19- Calculate The Number Of Sides Of A Regular Polygon, If: (I) Its Interior Angle Is Five Times Its Exterior Angle. (Ii) The Ratio Between Its Exterior Angle And Interior Angle Is 2:7. (Iii) Its Exterior Angle Exceeds Its Interior Angle By 60°. (I) Its Interior Angle Is Five Times Its Exterior Angle. (Ii) The Ratio Between Its Exterior Angle And Interior Angle Is 2:7. (Iii) Its Exterior Angle Exceeds Its Interior Angle By 60°. - 16: Understanding Shapes (Including Polygons) Class 8 Maths

Home Learn Fast select Course

Show Unit/Chapter Change Unit Change Subject Last Menu

ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

with Solutions - page 5

Qstn# B-19 Prvs-Qstn Next-Qstn

#19
Calculate the number of sides of a regular polygon, if: (i) its interior angle is five times its exterior angle. (ii) the ratio between its exterior angle and interior angle is 2:7. (iii) its exterior angle exceeds its interior angle by 60°. (i) its interior angle is five times its exterior angle. (ii) the ratio between its exterior angle and interior angle is 2:7. (iii) its exterior angle exceeds its interior angle by 60°.
Ans : Let number of sides of a regular polygon = n (i) Let exterior angle = x
Then interior angle = 5x
x + 5x = 180°
⇒ 6x = 180°
⇒ x = 180˚/6 = 30˚
∴ Number of sides(n) = 360˚/30 = 12 (ii) Ratio between exterior angle and interior angle = 2 : 7
Let exterior angle = 2x
Then interior angle = 7x
∴ 2x + 7x = 180˚
⇒ 9x = 180˚
⇒ x = 180˚/9
= 20˚
∴ Ext. angle = 2x = 2 × 20˚ = 40˚
∴ No. of sides = 360˚/40 = 9 (iii) Let interior angle = x
Then exterior angle = x + 60
∴ x + x + 60˚ = 180˚
⇒ 2x = 180˚ - 60˚ = 120˚
⇒ x = 120˚/2 = 60˚
∴ Exterior angle = 60˚ + 60˚ = 120˚
∴ Number of sides = 360˚/120˚ = 3 (i) Let exterior angle = x
Then interior angle = 5x
x + 5x = 180°
⇒ 6x = 180°
⇒ x = 180˚/6 = 30˚
∴ Number of sides(n) = 360˚/30 = 12 (ii) Ratio between exterior angle and interior angle = 2 : 7
Let exterior angle = 2x
Then interior angle = 7x
∴ 2x + 7x = 180˚
⇒ 9x = 180˚
⇒ x = 180˚/9
= 20˚
∴ Ext. angle = 2x = 2 × 20˚ = 40˚
∴ No. of sides = 360˚/40 = 9 (iii) Let interior angle = x
Then exterior angle = x + 60
∴ x + x + 60˚ = 180˚
⇒ 2x = 180˚ - 60˚ = 120˚
⇒ x = 120˚/2 = 60˚
∴ Exterior angle = 60˚ + 60˚ = 120˚
∴ Number of sides = 360˚/120˚ = 3

#19-i
its interior angle is five times its exterior angle.
Ans : Let exterior angle = x
Then interior angle = 5x
x + 5x = 180°
⇒ 6x = 180°
⇒ x = 180˚/6 = 30˚
∴ Number of sides(n) = 360˚/30 = 12

#19-ii
the ratio between its exterior angle and interior angle is 2:7.
Ans : Ratio between exterior angle and interior angle = 2 : 7
Let exterior angle = 2x
Then interior angle = 7x
∴ 2x + 7x = 180˚
⇒ 9x = 180˚
⇒ x = 180˚/9
= 20˚
∴ Ext. angle = 2x = 2 × 20˚ = 40˚
∴ No. of sides = 360˚/40 = 9

#19-iii
its exterior angle exceeds its interior angle by 60°.
Ans : Let interior angle = x
Then exterior angle = x + 60
∴ x + x + 60˚ = 180˚
⇒ 2x = 180˚ - 60˚ = 120˚
⇒ x = 120˚/2 = 60˚
∴ Exterior angle = 60˚ + 60˚ = 120˚
∴ Number of sides = 360˚/120˚ = 3