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Understanding Quadrilaterals and Practical Geometry — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSUnderstanding Quadrilaterals and Practical Geometry1 Mark
MCQ
In the given figure, $\text{ABCD}$ and $\text{BDCE}$ are parallelograms with common base $DC$. If $BC \perp BD$, then $\angle\text{BEC}=$

  • ✓
    $60^\circ$
  • B
    $30^\circ$
  • C
    $150^\circ$
  • D
    $120^\circ$
✓

Answer

Correct option: A.
$60^\circ$
$\angle\text{BCD}=30^\circ$
$\therefore\angle\text{BCD}=30^\circ$,
in $\triangle\text{CBD}$ by angle sum property of a triangle, we have
$\Rightarrow\angle\text{DBC}+\angle\text{BCD}+\angle\text{CDB}=180^\circ$
$\Rightarrow90^\circ+30^\circ+\angle\text{CDB}=180^\circ$
$\Rightarrow\angle\text{CDB}=180^\circ-120^\circ=60^\circ$
$\Rightarrow\angle\text{BEC}=60^\circ$

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