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Question
In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:
(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED
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Solution
(i) Since number of sides in the pentagon = 5
Each exterior angle = `360/5 = 72^circ`
∠BAE = 180° – 72°= 108°
(ii) In Δ ABE, 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°
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