MCQ
Mark $(\checkmark)$ against the correct answer.In a $\triangle\text{ABC},$ if $\angle\text{A}+\angle\text{B}=65^\circ$ and $\angle\text{B}+\angle\text{C}=140^\circ.$ Then, $\angle\text{B}={}?$
- ✓$25^\circ$
- B$35^\circ$
- C$40^\circ$
- D$45^\circ$
✓
Answer
Correct option: A.
$25^\circ$
In $\triangle\text{ABC,}$
$\angle\text{A}=65^\circ-\angle\text{B}$
$\angle\text{B}+\angle\text{C}=140^\circ$
$\angle\text{C}=140^\circ-\angle\text{B}$
But $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$(Angles of a triangle)
$\Rightarrow65^\circ-\angle\text{B}+140^\circ-\angle\text{B}+\angle\text{B}=180^\circ$
$\Rightarrow205^\circ-\angle\text{B}=180^\circ$
$\Rightarrow\angle\text{B}=205^\circ-180^\circ=25^\circ$
$\angle\text{A}=65^\circ-\angle\text{B}$
$\angle\text{B}+\angle\text{C}=140^\circ$
$\angle\text{C}=140^\circ-\angle\text{B}$
But $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$(Angles of a triangle)
$\Rightarrow65^\circ-\angle\text{B}+140^\circ-\angle\text{B}+\angle\text{B}=180^\circ$
$\Rightarrow205^\circ-\angle\text{B}=180^\circ$
$\Rightarrow\angle\text{B}=205^\circ-180^\circ=25^\circ$
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