Question

In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of:

(i) ∠BAE
(ii) ∠ABE
(iii) ∠BED

Answer 1

(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°