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Constructions — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSConstructions1 Mark
MCQ
Mark $(\checkmark)$ against the correct answer: In a $\triangle\text{ABC},$ If $A - B = 33^\circ $ and $B - C = 18^\circ ,$ then $\angle\text{B}=?$
  • A
    $35^\circ $
  • ✓
    $55^\circ $
  • C
    $45^\circ $
  • D
    $57^\circ $
✓

Answer

Correct option: B.
$55^\circ $
$\text{In}\ \triangle\text{ABC}:$
$A + B + C = 180^\circ .....(i)$
Given, $A - B = 33^\circ $
$A = 33^\circ + B .....(ii)$
$B - C = 18^\circ $
$C = B + 18^\circ .....(iii)$
Putting the values of $A$ and $B$ in equation $(i):$
$\Rightarrow B + 33^\circ + B + B - 18^\circ = 180^\circ $
$\Rightarrow 3B = 180^\circ - 15$
$\Rightarrow\text{B}=\frac{165^\circ}{3}=55^\circ$

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