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Triangles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsTriangles1 Mark
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Answer

  1. 104º
    Solution:

    $\triangle\text{ABC}$ is isosceles
    $\angle\text{ABC}=\angle\text{ACB}=52^\circ$
    then $\angle\text{BAC}=180^\circ-52^\circ-52^\circ=76^\circ$
    If $\text{AB}\parallel\text{CD},$ AC is transversal
    then $\angle\text{BAC}=\angle\text{ACD}$ (alternate angles)
    $\Rightarrow\angle\text{ACD}=76^\circ$
    Now from figure,
    $\angle\text{ACD}+\text{x}^\circ=180^\circ$
    $\Rightarrow\text{x}^\circ=180^\circ-76^\circ$
    $\Rightarrow\text{x}^\circ=104^\circ$
    Hence, correct option is (d).

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