ICSE-VIII-Mathematics
16: Understanding Shapes (Including Polygons) Class 8 Maths
- #14-i∠BAE (ii) ∠ABE (iii) ∠BED (ii) ∠ABE (iii) ∠BEDAns : Since number of sides in the pentagon = 5
Each exterior angle = 360/5 = 72°
∠BAE = 180° - 72°= 108°
(ii) In ΔABE, AB = AE
∴ ∠ABE = ∠AEB
But ∠BAE + ∠ABE + ∠AEB = 180˚
∴ 108˚ + 2∠ABE
= 180˚ - 108˚
= 72˚
⇒ ∠ABE = 36˚ (iii) Since ∠AED = 108˚
[∵ each interior angle = 108˚]
⇒ ∠AEB = 36˚
⇒ ∠BED = 108˚ - 36˚
= 72˚ (ii) In ΔABE, AB = AE
∴ ∠ABE = ∠AEB
But ∠BAE + ∠ABE + ∠AEB = 180˚
∴ 108˚ + 2∠ABE
= 180˚ - 108˚
= 72˚
⇒ ∠ABE = 36˚ (iii) Since ∠AED = 108˚
[∵ each interior angle = 108˚]
⇒ ∠AEB = 36˚
⇒ ∠BED = 108˚ - 36˚
= 72˚
- #14-ii∠ABEAns : In ΔABE, AB = AE
∴ ∠ABE = ∠AEB
But ∠BAE + ∠ABE + ∠AEB = 180˚
∴ 108˚ + 2∠ABE
= 180˚ - 108˚
= 72˚
⇒ ∠ABE = 36˚
- #14-iii∠BEDAns : Since ∠AED = 108˚
[∵ each interior angle = 108˚]
⇒ ∠AEB = 36˚
⇒ ∠BED = 108˚ - 36˚
= 72˚