MCQ
In figure, if $AB \| CD$, then $x =$
- ✓$100$
- B$105$
- C$110$
- D$114$
✓
Answer
Correct option: A.
$100$
Extending line $BA$ and $CP$ to meet at point $E.$
$\angle\text{APE}=180^\circ-148^\circ=32^\circ$
$\angle\text{EAP}=180^\circ-132^\circ=48^\circ$
$\angle\text{AEP}=\text{x}^\circ$ [(Correspondence angles) because $AB \| CD$ cut by transverse $EC]$
Now, in $\triangle\text{APE}$
$\angle\text{APE}+\angle\text{EAP}+\angle\text{AEP}=180^\circ$
$\Rightarrow\ 32^\circ+48^\circ+\text{x}^\circ=180^\circ$
$\Rightarrow\ \text{x}^\circ=100$
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
The value of $\{2-3(2-3)^3\}^3,$ is:
→$(x + 1)$ is a factor of the polynomial.
→Which one of the following is not the graphical representation of statistical data:
The point of the form (a, a) always lies on
In the given figure, $O$ is the centre of a circle in which $\angle\text{AOC}=100^\circ.$ Side $AB$ of quad. $OABC$ has been produced to $D.$ Then, $\angle\text{CBD}=?$
→If the total surface area of a right circular cone of slant height 13 cm is $90 \pi cm^2$, then the radius of its base is
→The positive square root of $7+\sqrt{48},$ is:
→IF $\text{AB}⊥\text{BC}$ and $\angle\text{BAC} = \angle\text{BCA},$ then which of the following statements is true?
→A diagonal of a parallelogram divides it into:
Which of the following point does not lie on the line $y = 2x + 3?$
→