Question

In the figure $AB=AC$, $BC=CD$ and DE | | BC. Find the measure of $\angle$ x.

• A. ${54}^{\circ }$
• B. ${61}^{\circ }$
• C. ${58}^{\circ }$
• D. ${72}^{\circ }$

Answer 1

The correct option is C ${58}^{\circ }$

Since, $AB=AC$

So, $\angle ABC=\angle ACB=P$ (Let.)

and $\angle ABC+\angle ACB=\angle CAF$ (Exterior angle property.)

So, $\angle ABC=\angle ACB=61°$

Also, $AB=AC$

and $DB=EC$

So, $DE\parallel BC$ (Mid-point theorem.)

Thus, $AD=AE$

So, $\angle ADE=\angle AED$

Now, in $△ADE$

$\angle ADE+\angle AED=\angle EAF=122°$

So, $\angle AED=\angle ADE=61°$

As, $BC=DC$

So, $\angle CBD=\angle CDB=61°$

now, $\angle ADE+\angle X+\angle CDB=180°$ (Linear fair)

so, $\angle x=180°-61°-61°=58°$