Question

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

Answer 1

In the given figure

∠BAC = ∠CED [Alternate angles]

⇒ ∠CED = 35°

In ∆CDE,

∠CDE + ∠DCE + ∠CED = 180° [Angle sum property of a triangle]

⇒ 53° + ∠DCE + 35° = 180°

⇒ ∠DCE + 88° = 180°

⇒ ∠DCE = 180° – 88° = 92°

Hence, ∠DCE = 92° Ans