MCQ
In Fig. if $\text{AB} || \text{CD}$, $\angle\text{ APQ} = 50^\circ$ and $\angle\text{PRD} = 130^\circ$, then $\angle\text{QPR}$ is: 
- A$130^\circ $
- B$50^\circ$
- ✓$80^\circ$
- D$30^\circ$
✓
Answer
Correct option: C.
$80^\circ$
Since, $AB$ and $CD$ are parallel and $PR$ is a transversal.
$\therefore\angle\text{BPR}+\angle\text{PRD}=180^\circ[\therefore$ Sum of consecutive interior angle is $180^\circ ]$
$\Rightarrow \angle \text{BPR} +130^\circ=180^\circ$
$[\therefore\angle\text{PRD}=130^\circ]$
$\Rightarrow\angle \text{BPR}=180^\circ-130^\circ$
$\Rightarrow \angle \text{BPR}=50^\circ$
Also, $\angle\text{APQ}+\angle \text{QPR}+\angle\text{BPR}=180^\circ$
$[\therefore$ sum of all the angies on a straight line is $180^\circ ]$
$\Rightarrow 50^\circ+\angle\text{QPR}+50^\circ=180^\circ$
$\Rightarrow\angle\text{QPR}+100^\circ=180^\circ$
$\Rightarrow\angle \text{QPR}=180^\circ-100^\circ$
$\therefore\angle\text{QPR}=80^\circ$
$\therefore\angle\text{BPR}+\angle\text{PRD}=180^\circ[\therefore$ Sum of consecutive interior angle is $180^\circ ]$
$\Rightarrow \angle \text{BPR} +130^\circ=180^\circ$
$[\therefore\angle\text{PRD}=130^\circ]$
$\Rightarrow\angle \text{BPR}=180^\circ-130^\circ$
$\Rightarrow \angle \text{BPR}=50^\circ$
Also, $\angle\text{APQ}+\angle \text{QPR}+\angle\text{BPR}=180^\circ$
$[\therefore$ sum of all the angies on a straight line is $180^\circ ]$
$\Rightarrow 50^\circ+\angle\text{QPR}+50^\circ=180^\circ$
$\Rightarrow\angle\text{QPR}+100^\circ=180^\circ$
$\Rightarrow\angle \text{QPR}=180^\circ-100^\circ$
$\therefore\angle\text{QPR}=80^\circ$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If the diameter of a circle is equal to the diagonal of a square, then the ratio of their areas is:
If ${\frac{-3}{\text{x}} =\frac{\text{x}}{27}}$ then the value of, $x$ is .........
→If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio $2 : 3,$ then the smaller of two angles is :
→In $\triangle\text{ABC},$ $\angle\text{A}=50^{\circ},$$\angle\text{B}=70^{\circ}$ and bisector of $\angle\text{C}$ Meets $AB$ in $D$ figure. Measure of $\angle\text{ADC}$
is.
→is.
In Fig. $PA || BC || DT$ and $AB || DC$. Then, the values of a and b are respectively. 
→The ratio of $3\ m$ to $60\ cm$ is.
→On selling a pen for Rs. $100$, a shopkeeper gains Rs. $15$. The cost price of the pen is:
→The mean of first five natural numbers is:
A parallelogram has ______ lines of symmetry:
The standard from of $\frac{55}{-99}$ is:
→