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Constructions — Maths STD 7 — Question

Maharashtra BoardEnglish MediumSTD 7MathsConstructions1 Mark
MCQ
Mark $(\checkmark)$ against the correct answer.In the given figure, side $BC$ of $\triangle\text{ABC}$ is produced to $D$ such that $\angle\text{ABC}=70^\circ$ and $\angle\text{ACD}=130^\circ.$ Then, $\angle\text{BAC}={ ?}$
  • A
    $60^\circ$
  • ✓
    $50^\circ$
  • C
    $70^\circ$
  • D
    $35^\circ$
✓

Answer

Correct option: B.
$50^\circ$
In $\triangle\text{ABC,}$ side $BC$ is produced to $D$
$\angle\text{ABC}=70^\circ$ and $\angle\text{ACD}=120^\circ$
Ext. $\angle\text{ACD}=\angle\text{BAC}+\angle\text{ABC}$
$\Rightarrow120^\circ=\angle\text{BAC}+70^\circ$
$\Rightarrow\angle\text{BAC}=120^\circ-70^\circ=50^\circ$

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