MCQ
In the adjoining figure, if $QP \| RT$, then $x$ is equal to:
- A$55^\circ$
- ✓$75^\circ$
- C$65^\circ$
- D$70^\circ$
✓
Answer
Correct option: B.
$75^\circ$
$\angle\text{QPR}=\angle\text{PRT}=40^\circ$ (Alternate interior angles)
In $\triangle\text{QPR}$
$\angle\text{PQR}+\angle\text{QPR}+\angle\text{PRQ}=180\circ $ (Angle sum property)
$65^\circ+40^\circ+\text{x}^\circ=180^\circ$
$\text{x}^{\circ}=180^\circ-40^\circ-65^\circ$
$\text{x}^{\circ}=75$
In $\triangle\text{QPR}$
$\angle\text{PQR}+\angle\text{QPR}+\angle\text{PRQ}=180\circ $ (Angle sum property)
$65^\circ+40^\circ+\text{x}^\circ=180^\circ$
$\text{x}^{\circ}=180^\circ-40^\circ-65^\circ$
$\text{x}^{\circ}=75$
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