MCQ
In a quadrilateral ABCD, $\angle\text{A}+\angle\text{C}$ is 2 times $\angle\text{B}+\angle\text{D}$ If $\angle\text{A}=140^\circ$ and $\angle\text{D}=60^\circ$ then $\angle\text{B}=$
- A60°
- B80°
- C120°
- DNone of these.
✓
Answer
- 60°
Solution:
$\angle\text{A}+\angle\text{B}+\angle\text{C}+\angle\text{D}=360^\circ\dots(1)$
Now, $\angle\text{A}+\angle\text{C}=2(\angle\text{B}+\angle\text{D})$ (given) ...(2)
Also, $\angle\text{A}=140^\circ,\ \angle\text{D}=60^\circ$
Putting value of $(\angle\text{A}+\angle\text{C})$ from eq. (2) in eq. (1)
$2(\angle\text{B}+\angle\text{D})+\angle\text{B}+\angle\text{D}=360^\circ$
$3(\angle\text{B}+\angle\text{D})=360^\circ$
$\Rightarrow\angle\text{B}+\angle\text{D}=120^\circ$
$\Rightarrow\angle\text{B}+60^\circ=120^\circ$
$\Rightarrow\angle\text{B}=60^\circ$
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 $\text{x}=(7+4\sqrt{3})$ than $\Big(\text{x}+\frac{1}{\text{x}}\Big)=?$
→Which of the following needs a proof?
If a + b + c = 0, then $\frac{\text{a}^2}{\text{bc}}+\frac{\text{b}^2}{\text{ca}}+\frac{\text{c}^2}{\text{ab}}=$
→The sides of a triangle are in ratio 3 : 4 : 5. If the perimeter of the triangle is 84cm, then area of the triangle is:
Write the correct answer in the following:
Between two rational numbers.
Between two rational numbers.
- There is no rational number.
- There is exactly one rational number.
- There are infinitely many rational numbers.
- There are only rational numbers and no irrational numbers.
The simplest form of $1 . \overline{6}$ is
→The product of a non-zero rational number with an irrational number is
Which of the following is a polynomial?
→- $\sqrt[3]{\text{y}}+4$
- $\sqrt{\text{y}}-3$
- $\text{y}$
- $\frac{1}{\sqrt{\text{y}}}+7$
Two chords AB and CD of a circle intersect each other at a point E outside the circle. If AB = 11cm, BE = 3cm and DE = 3.5cm, then CD = ?
- 10.5cm
- 9.5cm
- 8.5cm
- 7.5cm
