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