Question

In a regular pentagon ABCDE, inscribed in a circle; find ratio between angle EDA and angle ADC.

Answer 1

Arc AE subtends ∠AOE at the centre and ∠ADE at the remaining part of the circle.

∴ `∠ADE = 1/2 ∠AOE`

= `1/2 xx 72^circ`

= 36°   ...[Central angle is a regular pentagon at O]

∠ADC = ∠ADB + ∠BDC

= 36° + 36°

= 72°

∴ ∠ADE : ∠ADC = 36° : 72° = 1 : 2