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Quadrilaterals — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsQuadrilaterals1 Mark
MCQ
In a parallelogram ABCD, if $\text{DAB} = 75^\circ$ and $\angle\text{DBC} = 60^\circ,$ then $\angle\text{BDC} =\ ?$
  • A
    50º
  • B
    45º
  • C
    65º
  • D
    75º
✓

Answer

  1. 45º
    Solution:

    We know that the opposite angles of a parallelogram are equal.
    Therefore, $\angle\text{BCD} = \angle\text{BAD} = 75^\circ...\ \text{(i)}$
    (i) Now, in $\triangle\text{BCD},$
    We have,
    $\angle\text{CDB} + \angle\text{DBC} + \angle\text{BCD} = 180^\circ$ [Since, sum of the angles of a triangle is 180º]
    $⇒ \angle\text{CDB} + 60^\circ + 75^\circ = 180^\circ$
    $⇒ \angle\text{CDB} + 135^\circ = 180^\circ$
    $⇒ \angle\text{CDB} = (180^\circ - 135^\circ) = 45^\circ$

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