MCQ
In Fig. if $AB || CD,$ then $x =$
- A$32$
- ✓$42$
- C$52$
- D$31$
✓
Answer
Correct option: B.
$42$
Construction: Draw a line $PQ$ parallel to $AB$ which is also parallel to $CD$
$\angle \text{CDP}+\text{Reflex}\angle \text{CDP}=360^\circ$ [Complete angle]
$\therefore \text{CDP}+249^\circ=360^\circ$
$\Rightarrow \angle \text{CDP}=111^\circ$
Since, $PQ || AB$
$\therefore \angle \text{BAP}=\angle \text{APQ}$ [Alternate angles]
$\Rightarrow \angle \text{BAP}=28^\circ$
Now, $\angle \text{APQ}+\angle \text{QPD}=\angle \text{APD}$
$\Rightarrow 28^\circ+\angle \text{QPD}=(2\text{x}+13)^\circ$
$\Rightarrow \angle \text{QPD}=(2\text{x}+13)^\circ-28^\circ$
Since, $PQ || CD$
$\therefore \angle \text{QPD}+\angle \text{CDP}=180^\circ$ [Angles on the same side of a transversal line are supplementary]
$\Rightarrow (2\text{x}+13)^\circ-286\circ+111^\circ=180^\circ$
$\Rightarrow 2\text{x}+13-28+111=180$
$\Rightarrow 2\text{x}=84$
$\Rightarrow \text{x}=42$
Hence, the correct answer is option $(b).$
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
An angle is one-fifth of its supplement. The measure of the angle is
8 × 8 – 8 =?
A dice is rolled. The probability of getting an even prime is:
When a right triangle of area $3$ is rotated $360^\circ $ about its shorter leg, the solid that results has a volume of $30$. Calculate the volume of the solid if the same right triangle is rotated about its longer leg.
→The value of $X$ such that $\frac{3}{8}$ and $\frac{\text{X}}{-24}$ are equivalent rational numbers is .......
→Find smallest of two supplementary angles, if they are in the ratio $7 : 11.$
→The number of terms in the expression 7 × 9 + 7 : ?
Punita wants to classify a triangle according to the given clue. Two angles of the triangle are complementary. What type of triangle is the one Punita wants to classify$?$
→Mark $(\checkmark)$ against the correct answer in the following:
$2\frac{1}{25}=?$
→$2\frac{1}{25}=?$
The sum of two integers is $24$. is one them is -9, then the other is:
→