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Triangles — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSTriangles1 Mark
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Answer

  1. 60°
    Solution:
    In $\triangle\text{ABC}, \ \text{AB} = \text{AC}$
    $⇒ \angle\text{ABC} = \angle\text{ACB}$
    Also, $\angle\text{ACD}=120^\circ$
    $⇒ \angle\text{ACB} = 180^\circ- \angle\text{ACD}$ (Linear pair)
    $⇒ \angle\text{ACB} = 180^\circ- 120^\circ = 60^\circ$
    $⇒ \angle\text{ABC} = 60^\circ$
    By using angle sum property, we have
    $\angle\text{ABC} + \angle\text{ACB} + \angle\text{BAC} = 180^\circ$
    $60^\circ + 60^\circ+ \angle\text{A} = 180^\circ$
    or, $\angle\text{A} = 180^\circ - 120^\circ= 60^\circ$

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