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Constructions — Maths STD 7 — Question

Maharashtra BoardEnglish MediumSTD 7MathsConstructions1 Mark
MCQ
Mark $(\checkmark)$ against the correct answer.In a $\triangle\text{ABC},$ if $\angle\text{A}-\angle\text{B}=33^\circ$ and $\angle\text{B}-\angle\text{C}=18^\circ.$ Then, $\angle\text{B}={}?$
  • A
    $35^\circ$
  • ✓
    $55^\circ$
  • C
    $45^\circ$
  • D
    $57^\circ $
✓

Answer

Correct option: B.
$55^\circ$
In $\triangle\text{ABC,}$
$\angle\text{A}-\angle\text{B}=33^\circ$ and $\angle\text{B}-\angle\text{C}=18^\circ.$
$\angle\text{A}=33^\circ+\angle\text{B}$ and $\angle\text{C}=\angle\text{B}-18^\circ$
But $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$\Rightarrow33^\circ+\angle\text{B}+\angle\text{B}+\angle\text{B}-18^\circ=180^\circ$
$\Rightarrow3\angle\text{B}=180^\circ-33^\circ+18^\circ=165^\circ$
$\Rightarrow\angle\text{B}=55^\circ$

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