Question

abcd is a square cde is an equilateral triangle drawn on the side cd find the measure of angle aed and angle eab​

Answer 1

Step-by-step explanation:

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Answer 2

$\underline{\bf Given} :$

• ABCD is a square.
• CDE is a equilateral triangle.

$\underline{\bf To \: find} :$

• ∠AED = ?
• ∠EAB = ?

$\underline{\bf Solution} :$

As, ABCD is a square.

Hence, All sides are equal and all angles are of 90°.

$\sf : \implies AB=BC=CD=DA\: -(i)$

Now, As, CDE is an equilateral triangle.

So, All sides are equal and all angles are of 60°

$\sf : \implies CD=DE=EC\: - (ii)$

From equation (i) and (ii) :

• AB = BC = CD = DE = AD = CE

$\pink{\sf Now, \: In\: \triangle ADE}$

• AD = DE (Proved)

∴ ∠DAE = ∠AED (opposite angles of equal sides are equal.)

Now, ∠ADE = ∠ADC - ∠EDC

We have :

• ∠ADC = 90°
• ∠EDC = 60°

By substituting values :

$\sf : \implies \angle ADE = 90\degree - 60\degree$

$\sf : \implies \angle ADE = 30\degree$

Now, ∠ADE + ∠DAE + ∠AED = 180° (By angle sum property)

We have :

• ∠ADE = 30° (Proved)
• ∠DAE = ∠AED (Proved)

By substituting values :

$\sf : \implies 30\degree +2 \angle AED=180\degree$

$\sf : \implies 2 \angle AED=180\degree- 30\degree$

$\sf : \implies 2 \angle AED=150\degree$

$\sf : \implies 2 \angle AED=\dfrac{150\degree}{2}$

$\sf : \implies\angle AED=75\degree$

$\pink{\underline{\boxed{\bf \angle AED=75\degree}}}$

Now, ∠EAB = ∠DAB - ∠DAE

We have :

• ∠DAB = 90°
• ∠DAE = 75°

By substituting values :

$\sf : \implies\angle EAB =90\degree-75\degree$

$\sf : \implies\angle EAB =15\degree$

$\pink{\underline{\boxed{\bf \angle EAB=15\degree}}}$

$\underline{\sf Hence,\: \pink{\angle AED= 75\degree} \: and \: \pink{\angle EAB= 15\degree}}$