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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 $\angle\text{A}=3\text{y}^\circ \angle\text{B}=\text{x}^\circ, \ \angle\text{C}=5\text{y}^\circ$ and $\angle\text{CBD}=7\text{y}^\circ.$ Then, the value of $x$ is:
  • ✓
    $60$
  • B
    $45$
  • C
    $50$
  • D
    $35$
✓

Answer

Correct option: A.
$60$
In the given figure $\angle\text{ACB}+\angle\text{ACD}=180^\circ$ (Linear pair of angles)
$\therefore 5\text{y}′+7\text{y}′=180^\circ$
$\Rightarrow 12y^{\circ} = 180^{\circ}$
$\Rightarrow y = 15 ...(i)$
In $\triangle\text{ABC},$
$\angle\text{A}+\angle\text{B}+\angle\text{ACB}=180^\circ$ (angle sum property)
$\therefore 3\text{y}′+\text{x}′+5\text{y}′=180^\circ$
$\Rightarrow x^{\circ}+8 y^{\circ}=180^{\circ}$
$\Rightarrow x^2+8 \times 15^{\circ}=180^{\circ}[\text { using (1)] }$
$\Rightarrow x^{\prime}+120^{\circ}=180^{\circ}$
$\Rightarrow x^{\circ}=180^{\circ}-120^{\circ}=60^{\circ}$
Thus, the value of $x$ is $60 $.

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