MCQ
$\angle \text{A}$ is an obtuse angle. The measure of $\angle \text{A}$ and twice its supplementary differ by $30^\circ .$ Then $\angle \text{A}$ can be:
- A$150^\circ $
- ✓$110^\circ $
- C$140^\circ $
- D$120^\circ $
✓
Answer
Correct option: B.
$110^\circ $
Supplementary of $\angle \text{A}=180^\circ-\angle \text{A}$
Now,
$\angle \text{A}+30^\circ=2(180^\circ-\angle \text{A})$
$\Rightarrow \angle \text{A}+30^\circ=360^\circ-2\angle \text{A}$
$\Rightarrow 3\angle \text{A}=360^\circ-30^\circ$
$\Rightarrow 3\angle \text{A}=330^\circ$
$\Rightarrow \angle \text{A}=110^\circ$
Hence, the correct answer is option $(b).$
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