MCQ
In a $\triangle \text{ABC},$ if $\angle \text{A}+\angle \text{B}=150^\circ$ and $\angle \text{B}+\angle \text{C}=75^\circ,$ then $\angle \text{B} =$
- A$35^\circ$
- ✓$45^\circ$
- C$55^\circ$
- D$25^\circ$
✓
Answer
Correct option: B.
$45^\circ$
$\angle \text{A}+\angle \text{B}+\angle \text{C}=180^\circ$ [Angle sum property of triangle]
$\Rightarrow 150^\circ+\angle \text{C}=180^\circ$
$\Rightarrow \angle \text{C}=30^\circ$
Now, $\angle \text{B}+\angle \text{C}=75^\circ$
$\Rightarrow \angle \text{B}+30^\circ=75^\circ$
$\Rightarrow \angle \text{B}=45^\circ$
Hence, the correct answer is option $(b).$
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