ABCDE is a regular pentagon, diagonal AD divides ∠CDE in two parts, ____ is the ratio of ∠ADE and ∠ADC.

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Detailed Solution

Figure shows the regular pentagon, with diagonal AD divides ∠CDE into two parts.
Interior angle θ of regular pentagon
(n−2)×180=n×θ [where n=5]
(5−2)×180=5×θ
540=5×θ
θ=108o

°

So, ∠BCD=108

°

Diagonal AD is parallel to side BC
Hence,
∠ADC=180−108= 72

°

∠ADE=108−∠ADC=108−72= 36

°

Hence, the required ratio ∠ADE:∠ADC = 36:72 = 1:2

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