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Triangles — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSTriangles1 Mark
Question
In a $\triangle\text{ABC},$ if $\text{AB}=\text{AC}$ and BC is produced to D such that $\angle\text{ACD}=100^\circ$ then $\angle\text{A}=$
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Answer

  1. 20°
    Solution:

    $\text{AB}=\text{AC}$
    $\Rightarrow\angle\text{ABC}=\angle\text{ACB}$ (Isoscles $\triangle$ Property)
    $\angle\text{ACB}=180^\circ-100^\circ=80^\circ$
    $\Rightarrow\angle\text{ABC}-=\angle\text{ACB}=80^\circ$
    $\angle\text{A}=180^\circ-\angle\text{ACB}-\angle\text{ABC}=180^\circ-80^\circ-80^\circ=20^\circ$
    Hence, correct option is (a).

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