Question

ABCDE is a regular pentagon. Diagonal AD divides angle CDE into two parts. find the ratio of angle ADE / ADC. ​

Answer 1

Given : ABCDE is a regular pentagon. Diagonal AD divides angle CDE into two parts.

To find : $\frac{\angle ADE}{\angle ADC}$

Explanation:

interior angle of the regular pentagon :

$(n-2)\times 180 = n \times \theta$

where n is the number of sides = 5

now ,

$\theta = 108^\circ$

diagonal  AD is parallel to teh side BC

hence ,

∠ADC = 180°- 108°

∠ADC = 72°

now,

∠ADE = 180°-∠ADC

∠ADE = 180°- 72°

∠ADE = 36°

therefore ,

$\frac{\angle ADE}{\angle ADC}= \frac{36}{72}\\\\\frac{\angle ADE}{\angle ADC}=\frac{1}{2}$

Hence , the required ratio is 1:2

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