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Circles — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsCircles1 Mark
MCQ
In the give figure, $\text{ABCD}$ is a cyclic quadrilateral in which $BC = CD$ and $\angle\text{CBD}=35^\circ.$ Then, $\angle\text{BAD}=?$
  • A
    $65^\circ$
  • ✓
    $70^\circ$
  • C
    $110^\circ$
  • D
    $90^\circ$
✓

Answer

Correct option: B.
$70^\circ$
$BC = BD \ [$Given$]$
$\angle\text{BDC}=\angle\text{CBD}=35^\circ \ [$Angle opposite equal sides are equal$]$
In $\triangle\text{BCD},$
$\angle\text{BCD}+\angle\text{BDC}+\angle\text{CBD}=180^\circ\ [$Angle sum property$]$
$\Rightarrow\ \angle\text{BCD}+35^\circ+35^\circ=180^\circ$
$\Rightarrow\ \angle\text{BCD}=110^\circ$
Since $\text{ABCD}$ is a cyclic quadrilateral,
$\angle\text{BAD}+\angle\text{BCD}=180^\circ$
$\Rightarrow\ \angle\text{BAD}+110^\circ=180^\circ$
$\Rightarrow\ \angle\text{BAD}=70^\circ$

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