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# In figure, if AB || DE , $$\angle{BAC}$$ = $$35^\circ$$ and $$\angle{CDE}$$ = $$53^\circ$$ , find $$\angle{DCE}$$.

We have, AB || DE,
Therefore, by alternate angles theorem, we get,

$$\angle{AED}$$ = $$\angle{BAE}$$

Also, given that, $$\angle{BAC}$$ = $$35^\circ$$ and $$\angle{BAC}$$ = $$\angle{BAE}$$

$$\therefore$$ , $$\angle{AED}$$ = $$35^\circ$$

Now, in $$\triangle{DCE}$$,
$$\angle{DCE}$$ + $$\angle{CED}$$ + $$\angle{CDE}$$ = $$180^\circ$$

because, Sum of all angles of triangle is equal to 180.
Thus, by putting given values, we get,

$$\Rightarrow$$ $$\angle{DCE}$$ + $$35^\circ$$ + $$53^\circ$$ = $$180^\circ$$
$$\Rightarrow$$ $$\angle{DCE}$$ = $$180^\circ$$ - $$88^\circ$$
$$\Rightarrow$$ $$\angle{DCE}$$ = $$92^\circ$$