In the given figure $$\triangle$$ABC, if $$\theta$$ = $$80^\circ$$, the measure of each of the other two angles will be:

Angles opposite to equal sides in a triangle are equal.

In $$\triangle$$ABC, AC = AB

$$\Rightarrow$$  $$\angle$$ABC = $$\angle$$ACB

Let $$\angle$$ABC = $$\angle$$ACB = x

In $$\triangle$$ABC,

$$\angle$$ABC + $$\angle$$ACB + $$\angle$$BAC = $$180^\circ$$

$$\Rightarrow$$  x + x + $$\theta$$ = $$180^\circ$$

$$\Rightarrow$$  2x + $$80^\circ$$ = $$180^\circ$$

$$\Rightarrow$$  2x = $$100^\circ$$

$$\Rightarrow$$  x = $$50^\circ$$

$$\Rightarrow$$  $$\angle$$ABC = $$\angle$$ACB = $$50^\circ$$

Hence, the correct answer is Option C