In △ABC point D is on side BC such that AD = BD and AB = DC = AC. Find all the angles of △ABC.

Step-by-step explanation:

In , sides AB = AC.

We know the property that angles opposite to equal sides in a triangle are equal.

Hence,  

Let this angle be x.

So,

Similarly, in

Hence,

and are same.

By equation (1):

Similarly, in :

Let this angle be y.

We know that sum of all three angles in a triangle is equal to .

In , sum of all three angles:

In , sum of all three angles:

Using elimination method to solve equation (4) and (5):

Multiplying equation (5) by 2 and subtracting (4) from it:

Putting value of x in (4):

So, angles of are:

x, (x+y) and y

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