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# In figure, $$\angle{ABC}$$ = $$69^\circ$$, $$\angle{ACB}$$ = $$31^\circ$$. Find $$\angle{BDC}$$.

As we know that, the angles in the same segment are equal.
We get,

$$\angle{BDC}$$ = $$\angle{BAC}$$ ...(i)

Now, in $$\triangle{ABC}$$,

$$\angle{BAC}$$ + $$\angle{ABC}$$ + $$\angle{ACB}$$ = $$180^\circ$$
$$\Rightarrow$$ $$\angle{BAC}$$ + $$69^\circ$$ + $$31^\circ$$ = $$180^\circ$$
$$\Rightarrow$$$$\angle{ABC}$$ + $$100^\circ$$ = $$180^\circ$$
$$\Rightarrow$$ $$\angle{ABC}$$ = $$180^\circ$$ - $$100^\circ$$
$$\therefore$$ $$\angle{BAC}$$ = $$80^\circ$$
$$\therefore$$ $$\angle{BDC}$$ = $$80^\circ$$ ...(from (i))