MCQ
In Fig. $\text{ABC}$ ids an isosceles triangle whose side $AC$ is produced to $E$. Through $C, CD$ is drawn parallel to $BA$. The value of $x$ is: 
- A$52^\circ$
- B$76^\circ$
- C$156^\circ$
- ✓$104^\circ$
✓
Answer
Correct option: D.
$104^\circ$
$\triangle\text{ABC}$ is isosceles
$\angle\text{ABC}=\angle\text{ACB}=52^\circ$
then $\angle\text{BAC}=180^\circ-52^\circ-52^\circ=76^\circ$
If $\text{AB}\parallel\text{CD}, AC$ is transversal
then $\angle\text{BAC}=\angle\text{ACD}\ ($alternate angles$)$
$\Rightarrow\angle\text{ACD}=76^\circ$
Now from figure,
$\angle\text{ACD}+\text{x}^\circ=180^\circ$
$\Rightarrow\text{x}^\circ=180^\circ-76^\circ$
$\Rightarrow\text{x}^\circ=104^\circ$
Hence, correct option is $(d)$.
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