MCQ
$ABCD$ is a parallelogram in which diagonal $AC$ bisects $\angle\text{BAD}.$ if $\angle\text{BAC}=35^\circ,$ then $\angle\text{ABC}=$
- A$70^\circ $
- ✓$110^\circ$
- C$90^\circ$
- D$120^\circ$
✓
Answer
Correct option: B.
$110^\circ$
$AC$ bisects $\angle\text{DAB}.$
$\Rightarrow\angle\text{DAC}=\angle\text{BAC}=35^\circ$
$\Rightarrow\angle\text{BAD}=2\times35^\circ=70^\circ$
$\angle\text{A}+\angle\text{B}=180^\circ ($Sum of any two adjacent angles in parallelogram $=180^\circ )$
$\Rightarrow\angle\text{B}=\angle\text{ABC}=180^\circ-\angle\text{BAD}$
$=180^\circ-70^\circ=110^\circ$
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