MCQ
In $\triangle A B C$, if $\angle A=65^{\circ}$ and $\angle C=85^{\circ}$, then $\angle B=$ ?
- A$25^{\circ}$
- ✓$30^{\circ}$
- C$35^{\circ}$
- D$40^{\circ}$
✓
Answer
Correct option: B.
$30^{\circ}$
(b) $30^{\circ}$
Hint. $(\angle A+\angle B)+(\angle B+\angle C)=\left(65^{\circ}+140^{\circ}\right) \Rightarrow(\angle A+\angle B+\angle C)+B=205^{\circ} \Rightarrow 180^{\circ}+\angle B=205^{\circ} $
$ \Rightarrow \angle B=205^{\circ}-180^{\circ}=25^{\circ}.$
Hint. $(\angle A+\angle B)+(\angle B+\angle C)=\left(65^{\circ}+140^{\circ}\right) \Rightarrow(\angle A+\angle B+\angle C)+B=205^{\circ} \Rightarrow 180^{\circ}+\angle B=205^{\circ} $
$ \Rightarrow \angle B=205^{\circ}-180^{\circ}=25^{\circ}.$
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