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Triangles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsTriangles1 Mark
MCQ
Line sgements AB and CD intersect at O such that $\text{AC}||\text{DB}.$ If $\angle\text{CAB} = 45^\circ$ and $\angle\text{CDB} = 55^\circ,$ then $\angle\text{BOD} =$
  • A
    80°
  • B
    90°
  • C
    100°
  • D
    135°
✓

Answer

  1. 80°
    Solution:

    $\text{AC}||\text{DB}$
    And, AB is transverse to these parallel lines
    So, $\angle\text{CAB} = \angle\text{ABD}$ (Alternate angles)
    $⇒\angle\text{ABD} = 45^\circ$
    Now In $\triangle\text{BOD}$
    $\angle\text{BOD} + \angle\text{ODB} + \angle\text{DBA} = 180^\circ$
    $\angle\text{DBA} = \angle\text{ABD} = 45^\circ, \ \angle\text{ODB} = 55^\circ$
    So, $\angle\text{BOD} = 180^\circ - 45^\circ - 55^\circ$
    $= 80^\circ$

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