MCQ
Mark $(\checkmark)$ against the correct answer.In the given figure, $\text{PQ}\parallel\text{RS,}\angle\text{PAB}=60^\circ$ and $\angle\text{ACS}=100^\circ.$ Then $\angle\text{BAC}={}?$
- ✓$40^\circ$
- B$60^\circ$
- C$80^\circ$
- D$50^\circ$
✓
Answer
Correct option: A.
$40^\circ$
In the given figure,
$\text{PQ}\parallel\text{RS,}$
$\angle\text{PAB}=60^\circ$ and $\angle\text{ACS}=100^\circ$
$\text{PQ}\parallel\text{RS}$
$\angle\text{ABC}=\angle\text{PAB}$ (alternate angles) $60^\circ$
But Ext. $\angle\text{ACS}=\angle\text{BAC}+\angle\text{ABC}$
$\Rightarrow100^\circ\angle\text{BAC}+60^\circ$
$\Rightarrow\angle\text{BAC}=100^\circ-60^\circ=40^\circ$
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