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Triangles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsTriangles1 Mark
MCQ
In the given figure, side $BC$ of $\triangle\text{ABC}$ has been produced to a point $D.$ If $\angle\text{A}=3\text{y},\angle\text{B}=\text{x}^\circ,\angle\text{C}=5\text{y}^\circ$ and $\angle\text{CBD}=7\text{y}^\circ.$ Then, the value of $x$ is:
  • ✓
    $60$
  • B
    $50$
  • C
    $45$
  • D
    $35$
✓

Answer

Correct option: A.
$60$
$\angle\text{ACB}=\angle\text{ACD}=180^\circ$ (linear pair)
$\Rightarrow5\text{y}+7\text{y}=180^\circ$
$\Rightarrow12\text{y}=180^\circ$
$\Rightarrow\text{y}=15^\circ$
Now, $\angle\text{ACD}=\angle\text{ABC}+\angle\text{BAC}$ (Exterior angle property)
$\Rightarrow7\text{y}=\text{x}+3\text{y}$
$\Rightarrow7(15^\circ)=\text{x}+3(15^\circ)$
$\Rightarrow105^\circ=\text{x}+45^\circ$
$\Rightarrow\text{x}=60^\circ$

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