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.
$110^\circ$
Given,
$ABCD$ is a parallelogram
Diagonal AC bisects $\angle\text{BAD}$
$\angle\text{BAC} = 35^\circ$
$∵ \angle\text{A} + \angle\text{B} = 180^\circ ...\text{(i)}$ [angle sum property of quadrilateral]
$\angle\text{A} = 2\angle\text{BAC} = 2 × 35^\circ = 70^\circ$
Putting value of $\angle\text{A}$ in equation (i)
$70^\circ + \angle\text{B} = 180^\circ$
$\angle\text{B} = 180^\circ - 70^\circ = 110^\circ$
$\angle\text{ABC} = 110^\circ$
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