In the figure, if AB∥DE, ∠BAC=35° and ∠CDE=53°, find ∠DCE.

Given, AB∥DE, ∠BAC=35°, ∠CDE=53°
According to the question,
∠BAC=∠CED (Alternate interior angles)
∴∠CED=35°
Now, ∠DCE+∠CED+∠CDE=180° (Sum of the interior angles of the triangle)
⇒∠DCE+35°+53°=180°
⇒∠DCE+88°=180°
⇒∠DCE=92°