Question
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 $\angle\text{B}=$
  1. 60°
  2. 80°
  3. 120°
  4. None of these.

Answer

  1. 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)

$2(\angle\text{B}+\angle\text{D})+\angle\text{B}+\angle\text{D}=360^\circ$

$3(\angle\text{B}+\angle\text{D})=360^\circ$

$\Rightarrow\angle\text{B}+\angle\text{D}=120^\circ$

$\Rightarrow\angle\text{B}+60^\circ=120^\circ$

$\Rightarrow\angle\text{B}=60^\circ$

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