MCQ
In Fig. if $\text {DC}\parallel\text{DC}$ and $\text{AB}=\text{AC},$ the value of $\angle\text{ABD}$ is:
- A70º
- ✓110º
- C120º
- D130º
✓
Answer
Correct option: B.
110º
If $\text{AE}\parallel\text{DC}$ and AC is transversal,
then $\angle\text{FAC}=70^\circ$ (opposite angles)
Also $\angle\text{FAC}-=\angle\text{ACB}=70^\circ$ (Alternate angles)
Since $\text{AB}=\text{AC},\triangle\text{ABC}$ is isosceles.
So $\angle\text{ABC}=\angle\text{ACB}$
$\Rightarrow\angle\text{ABC}=70^\circ$
Now $\angle\text{ABD}=180^\circ-\angle\text{ABC}=180^\circ-70^\circ=100^\circ$
Hence, correct option is (b).
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