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Quadrilaterals — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsQuadrilaterals1 Mark
MCQ
ABCD is a Parallelogram in which $\angle\text{BAO}=35^\circ, \ \angle\text{DAO}=40^\circ$ and $\angle\text{COD}=105^\circ.$ Find $\angle\text{ABO}=\ ?$
  • A
    45º
  • B
    30º
  • C
    20º
  • D
    40º
✓

Answer

  1. 40º
    Solution:

    Given, ABCD is a parallelogram having $\angle\text{BAO}=35^\circ, \ \angle\text{DAO}=40^\circ$ and $\angle\text{COD}=105^\circ.$
    Now, $\angle\text{COD} = \angle\text{AOB} = 105^\circ$ [vertically opposite angles]
    In $\angle\text{ABO},$ by angle sum property of triangle,
    $⇒ \angle\text{AOB} + \angle\text{OAB} + \angle\text{ABO} = 180^\circ$
    $⇒ 105^\circ + 35^\circ + \angle\text{ABO} = 180^\circ$
    $⇒ \angle\text{ABO} = 40^\circ$

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