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Triangles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsTriangles1 Mark
MCQ
In $\triangle\text{ABC}, \ \angle\text{B} = \angle\text{C}$ and ray AX bisects the exterior angle $\triangle\text{DAC}.$ If $\triangle\text{DAX} = 70^\circ,$ then $\angle\text{ACB} =$
  • A
    55º
  • B
    35º
  • C
    70º
  • D
    90º
✓

Answer

  1. 70º
    Solution:

    AX is bisector of $\triangle\text{DAC}$
    $\Rightarrow\ \angle\text{DAX}=\angle\text{XAC}=70^\circ$
    $\Rightarrow\ \angle\text{DAC}=2\times70=140^\circ$
    Now, $\angle\text{A} = 180^\circ - \angle\text{DAC} = 180^\circ\text{c}- 180° = 40^\circ$
    In $\triangle\text{ABC}$
    $\angle\text{A} + \angle\text{B} + \angle\text{C} = 180^\circ$
    $\Rightarrow\ 40^\circ + \angle\text{B} + \angle\text{C}= 180^\circ$
    $\Rightarrow\ 40^\circ + \angle\text{C} + \angle\text{C}= 180^\circ...(\angle\text{B} = \angle\text{C})$
    $\Rightarrow\ 2\angle\text{C} = 140^\circ$
    $\Rightarrow\ \angle\text{C} = 70^\circ$
    i.e. $\angle\text{ACB} = 70^\circ$

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