Question

In the given figure AD = BD = AC; ZCAE = 75º and ZACD = xº. Find the value of x.​

Answer 1

Answer:

y = 25 degree   x=50 degree

Step-by-step explanation:

This is how the figure will look like.

Since AC = AD in △ACD, let  ∠ACD =∠ADC =x

Theorem: In a triangle, angles opposite to equal sides are also equal.

Similarly, in △ABD, BD = AD

Let  ∠ABD =∠ADB =y

Theorem:  Exterior angle of a triangle at a vertex is equal to the sum of the opposite interior angles.

Since ∠EAC=75o  is an  exterior angle, ∠EAC =∠ABD+∠ACD  

⇒ x+y =75o  ------ (1)

Similarly, ∠ADC is an exterior angle at D in the △ADB

⇒ ∠ADC =∠DBA+∠DAB

x=y+y=2y  -----(2)

Solving equation (1) and (2), we get:

x=50° andy=25°

Therefore, ∠ACD=x=50°

Answer 2

Answer:

x=50°

Step-by-step explanation:

Since AC = AD in △ACD, let  ∠ACD =∠ADC =x

Theorem: In a triangle, angles opposite to equal sides are also equal.

Similarly, in △ABD, BD = AD

Let  ∠ABD =∠ADB =y

Theorem:  Exterior angle of a triangle at a vertex is equal to the sum of the opposite interior angles.

Since ∠EAC=75o  is an  exterior angle, ∠EAC =∠ABD+∠ACD  

⇒ x+y =75o  ------ (1)

Similarly, ∠ADC is an exterior angle at D in the △ADB

⇒ ∠ADC =∠DBA+∠DAB

x=y+y=2y  -----(2)

Solving equation (1) and (2), we get:

x=50° andy=25°

Therefore, ∠ACD=x=50°