MCQ
In the figure, $AB \| CD$. If $\angle\text{APQ}=70 ^\circ$ and $\angle\text{PRD}=120^\circ$ then $\angle\text{QPR}=?$
- ✓$55^\circ$
- B$60^\circ$
- C$40^\circ$
- D$35^\circ$
✓
Answer
Correct option: A.
$55^\circ$
Since $AB \| CD,$
$\angle\text{APQ}=\angle\text{PQR}=70^\circ$ (Alternate angles)
$\Rightarrow\angle\text{PRD}=\angle\text{PQR}+\angle\text{QPR}$ (Exterior angle is equal to sum of the remote interior angles)
$\Rightarrow120^\circ=70^\circ+\angle\text{QPR}$
$\Rightarrow\angle\text{QPR}=506^\circ$
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