MCQ
In the given figure, $\text{ABCD}$ is a kite, the value of angle $x$ is
- A$86^{\circ}$
- B$100^{\circ}$
- ✓$104^{\circ}$
- Dnone of these
✓
Answer
Correct option: C.
$104^{\circ}$
In the given figure, $\text{ABCD}$ is a kite whose
diagonals $AC$ and $BD$ intersect at $O$ at right angles.
$\text { In } \triangle \text{OAB,} \angle O=90^{\circ}$
$\therefore \angle \text{OAB}+\angle A B O=90^{\circ}$
$\Rightarrow \angle \text{OAB}+36^{\circ}=90^{\circ}$
$\Rightarrow \angle \text{OAB}=90^{\circ}-36^{\circ}=54^{\circ}$
$\text { But } \angle \text{OAD}=\angle \text{OCD}=50^{\circ}$
$x=\angle \text{DAO} +\angle \text{AOB}$
$\Rightarrow x=50^{\circ}+54^{\circ}=104^{\circ}$
diagonals $AC$ and $BD$ intersect at $O$ at right angles.
$\text { In } \triangle \text{OAB,} \angle O=90^{\circ}$
$\therefore \angle \text{OAB}+\angle A B O=90^{\circ}$
$\Rightarrow \angle \text{OAB}+36^{\circ}=90^{\circ}$
$\Rightarrow \angle \text{OAB}=90^{\circ}-36^{\circ}=54^{\circ}$
$\text { But } \angle \text{OAD}=\angle \text{OCD}=50^{\circ}$
$x=\angle \text{DAO} +\angle \text{AOB}$
$\Rightarrow x=50^{\circ}+54^{\circ}=104^{\circ}$
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
A student was asked to find $\frac{7}{8}$ of a positive number. He found $\frac{7}{18}$ of the same by mistake.If his answer was 770 less than the correct one, then the original number was
→A coloured cloth 1.75 m long and 105 cm wide is made into square handkerchiefs of side 35 cm. The number of handkerchiefs made is
If $2^{12}-2^{10}=3 \times 2^x$, then the value of $x$ is:
→The probability that a letter chosen at random from the letters of the word PORCUPINE is a vowel is:
If the sum of all interior angles of a polygon is $1260^\circ,$ then number of sides of polygon is
→By selling an article for $₹ 240$, a trader loses $4 \%$. In order to gain $10 \%$ he must sell that article for
→In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. A student attempted all the 200 questions and scored in all 200 marks. The number of questions he answered correctly was
If ₹ 64 amount to ₹ 83.20 in 2 years, what will ₹ 86 amount to in 4 years at the same rate per cent per annum?
If $\left(x^2+\frac{1}{x^2}\right)=102$, then the value of $\left(x-\frac{1}{x}\right)$ is
→Probability of getting a non-red ball from a bag containing $4$ red, $5$ blue and $3$ black balls is
→