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Lines and Angles — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSLines and Angles1 Mark
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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