3. In Fig. 6.41, if AB || DE, ∠BAC = 35° and ∠CDE = 53°, find ∠DCE.
Solution: We know that AE is a transversal since AB || DE Here ∠BAC and ∠AED are alternate interior angles. Hence, ∠BAC = ∠AED It is given that ∠BAC = 35° ∠AED = 35° Now consider the triangle CDE. We know that the sum of the interior angles of a triangle is 180°. ∴ ∠DCE+∠CED+∠CDE = 180° Putting the values, we get ∠DCE+35°+53° = 180° Hence, ∠DCE = 92°
