Question

If $AB\parallel CD$ then find the value of x.

• A. ${100}^o$
• B. ${120}^o$
• C. ${160}^o$
• D. ${140}^o$

Answer 1

The correct option is D ${140}^o$

Given-

The lines AB & CD are parallel to each other.

AE & CE meet at E.

$\angle EAB={108}^o,\angle ECD={112}^o.$

To find out-

$\angle AEC=?$

Solution-

the line EF is drawn such that

$EF\parallel ABi.eEF\parallel CD\because AB\parallel CD.$

Now the sum of the same side internal angles=${180}^o$

$\therefore \angle AEF={180}^o-\angle EAB={180}^o-{108}^o={72}^o\&\angle CEF={180}^o-\angle ECD={180}^o-{112}^o={68}^o.\therefore \angle AEC=x=\angle AEF+\angle CEF={72}^o+{68}^o={140}^o.$

Ans- Option D.