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,

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