Qstnid -A-5- (I) If All The Angles Of A Hexagon Are Equal; Find The Measure Of Each Angle. (Ii) If All The Angles Of A 14-sided Figure Are Equal; Find The Measure Of Each Angle. - 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

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#5
(i) If all the angles of a hexagon are equal; find the measure of each angle. (ii) If all the angles of a 14-sided figure are equal; find the measure of each angle.
Ans : (i) No. of sides of hexagon, n = 6
Let each angle be = x°
Sum of angles = 6x°
(n - 2)× 180° = Sum of angles
⇒ (6 - 2)× 180° = 6x°
⇒ 4× 180 = 6x
⇒ x = (4 × 180)/6
⇒ x = 120˚
∴ Each angle of hexagon = 120˚ (ii) No. of sides of polygon, n = 14
Let each angle = x˚
∴ Sum of angles = 14x˚
∴ (n - 2) × 180˚ = Sum of angles of polygon
∴ (14 - 2) × 180˚ = 14x
12 × 180˚ = 14x
⇒ x = (12 × 180)/14
⇒ x = 1080/7
⇒ x = (154 2/7)˚

#5-i
If all the angles of a hexagon are equal; find the measure of each angle.
Ans : No. of sides of hexagon, n = 6
Let each angle be = x°
Sum of angles = 6x°
(n - 2)× 180° = Sum of angles
⇒ (6 - 2)× 180° = 6x°
⇒ 4× 180 = 6x
⇒ x = (4 × 180)/6
⇒ x = 120˚
∴ Each angle of hexagon = 120˚

#5-ii
If all the angles of a 14-sided figure are equal; find the measure of each angle.
Ans : No. of sides of polygon, n = 14
Let each angle = x˚
∴ Sum of angles = 14x˚
∴ (n - 2) × 180˚ = Sum of angles of polygon
∴ (14 - 2) × 180˚ = 14x
12 × 180˚ = 14x
⇒ x = (12 × 180)/14
⇒ x = 1080/7
⇒ x = (154 2/7)˚