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Circles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCircles1 Mark
MCQ
In the given figure, if $\angle\text{AOD}=135^\circ$ then $\angle\text{BOC}$ is equal to :
  • A
    $25^\circ$
  • ✓
    $45^\circ$
  • C
    $52.5^\circ$
  • D
    $62.5^\circ$
✓

Answer

Correct option: B.
$45^\circ$
We know that sum of the angles subtended by opposite sides of a quadrilateral having a circumscribed circle is $180^\circ .$
$\Rightarrow\angle\text{AOD}+\angle\text{BOC}=180^\circ$
$\Rightarrow135^\circ+\angle\text{BOC}=180^\circ$
$\Rightarrow\angle\text{BOC}=45^\circ$

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