Lets write the measurement of ∠ABC and ∠ACB if AB = AC.

Given: ΔABC, ∠BAC = 80° and AB = AC

To find the measurement of ∠ABC and ∠ACB

Now in ΔABC, it is given AB = AC

We know angles opposite to equal sides are equal, therefore

⇒∠ACB = ∠ABC………(i)

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(i) and given criteria, we get

80° + ∠ABC + ∠ABC = 180°

⇒ 80° + 2∠ABC = 180°

⇒ 2∠ABC = 180° - 80°

⇒ 2∠ABC = 100°

⇒ ∠ABC = 50°

Substituting the above value in equation (i) we get

⇒∠ACB = ∠ABC = 50°

These are the required values of the angles.