MCQ
In the given figure $ABCD$ is a cyclic quadrilateral in which $AB || DC$ and $\angle\text{BAD}=100^\circ.$ Then, $\angle\text{ABC}=?$
- A$80^\circ$
- ✓$100^\circ $
- C$50^\circ$
- D$40^\circ$
✓
Answer
Correct option: B.
$100^\circ $
Since $AB || DC,$
$\angle\text{ADC}+\angle\text{BAD}=180^\circ$
$\Rightarrow\ 100^\circ+\angle\text{BAD}=180^\circ$
$\Rightarrow\ \angle\text{BAD}=80^\circ$
We know that the opposite angles of a quadrilateral are supplementary.
$\angle\text{BAD}+\angle\text{ABC}=180^\circ$
$\Rightarrow\ 80^\circ+\angle\text{ABC}=180^\circ$
$\Rightarrow\ \angle\text{ABC}=100^\circ$
$\angle\text{ADC}+\angle\text{BAD}=180^\circ$
$\Rightarrow\ 100^\circ+\angle\text{BAD}=180^\circ$
$\Rightarrow\ \angle\text{BAD}=80^\circ$
We know that the opposite angles of a quadrilateral are supplementary.
$\angle\text{BAD}+\angle\text{ABC}=180^\circ$
$\Rightarrow\ 80^\circ+\angle\text{ABC}=180^\circ$
$\Rightarrow\ \angle\text{ABC}=100^\circ$
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