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

Question

In Fig. 6.41, if AB || DE, &#x2220; BAC = 35&#xB0; and &#x2220; CDE = 53&#xB0;, find &#x2220; DCE.

Philoid · Accepted Answer

It is given in the question that:

AB parallel DE,

∠BAC = 35^o

And,

∠CDE = 53^o

According to question,

∠BAC = ∠CED (Alternate interior angles)

Therefore,

∠CED = 35^o

Now,

∠DCE + ∠CED + ∠CDE = 180^o (Sum of the interior angles of the triangle)

∠DCE + 35^o + 53^o = 180^o

∠DCE + 88^o = 180^o

∠DCE = 92^o