Let’s write the measurement of angles of triangle ABC if AB = BC and ∠BAC + ∠ACB = 50°

Given: ΔABC, ∠BAC + ∠ACB = 50° and AB = BC

To find the measurement of angles of the triangle ABC

Now in ΔABC, it is given AB = BC

We know angles opposite to equal sides are equal, therefore

⇒∠BAC = ∠ACB……….(i)

Given ∠BAC + ∠ACB = 50°

Substituting values from equation (i) in the above equation, we get

⇒∠ACB + ∠ACB = 50°

⇒2∠ACB = 50°

⇒∠ACB = 25°…….(ii)

Substituting values from equation (ii) in equation (i), we get

⇒∠BAC = ∠ACB = 25°……….(iii)

We also know in a triangle the sum of all three interior angles is equal to 180°.

So in this case,

∠BAC + ∠ACB + ∠ABC = 180°

Substituting the values from equation(iii) and given criteria, we get

∠ABC + 25° + 25° = 180°

⇒ ∠ABC = 180° - 25° - 25°

⇒ ∠ABC = 130°……(iv)

From equation (iii) and (iv), the required values of the angles are

∠BAC = ∠ACB = 25°, ∠ABC = 130°