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