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Quadrilaterals — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsQuadrilaterals1 Mark
MCQ
In the given figure $, \text{ABCD}$ is a parallelogram in which $\angle\text{BDC}=45^{\circ}$ and $\angle\text{BAD}=75^{\circ}.$ Then, $\angle\text{CBD}=?$
  • A
    $45^\circ$
  • B
    $55^\circ$
  • ✓
    $60^\circ$
  • D
    $75^\circ$
✓

Answer

Correct option: C.
$60^\circ$
Since $\text{ABCD}$ is a parallelogram $, AB \| CD$ since opposite angles of a parallelogram are equal.
$\Rightarrow\angle\text{ABD}=\angle\text{BCD}=45^{\circ} ...($Alternate angles$)$
In $\triangle\text{ADB},$
$\angle\text{ABD}+\angle\text{BDA}+\angle\text{DAB}=180^{\circ} ... ($Angle sum property$)$
$\Rightarrow45+\angle\text{BDA}+75=180$
$\Rightarrow\angle\text{BDA}+120=180$
$\Rightarrow\angle\text{BDA}=60^{\circ}$
$\Rightarrow\angle\text{CBD}=\angle\text{BDA}=60^{\circ} ... ($Alternate angles$)$
$\Rightarrow\angle\text{CBD}=60^{\circ}$

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