In Fig. 6.41, if AB || DE, ∠ BAC = 35° and ∠ CDE = 53°, find ∠ DCE.

 

 

 

 

 

 

 

 Fig. 6.41

Given: AB || DE, ∠BAC = 35° and ∠CDE = 53°

To find: ∠DCE

According to angle sum property of a triangle, sum of the interior angles of a triangle is 180°.

Since, AB || DE and AE is the transversal,

∠DEC = ∠BAC [Alternate interior angles]

Thus, ∠DEC = 35°

Now, in △CDE

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

53° + 35° + ∠DCE = 180°

∠DCE = 180° - 88°

Thus, we have ∠DCE = 92°.