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Q.

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

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