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Lines and Angles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsLines and Angles1 Mark
MCQ
In the given figure, straight lines $AB$ and $CD$ intersect at $O$. If $\angle\text{AOC}=\phi,\angle\text{BOC}=\theta$ and $\theta=3\phi,$ then $\phi=?$
  • ✓
    $45^\circ$
  • B
    $30^\circ$
  • C
    $60^\circ$
  • D
    $40^\circ$
✓

Answer

Correct option: A.
$45^\circ$
We have.
$\theta+\phi=180^\circ$ [$\because AOD$ is a straight line]
$\Rightarrow3\phi+\phi=180^\circ [\because\theta=3\phi]$
$\Rightarrow4\theta=180^\circ$
$\Rightarrow\phi=45^\circ.$

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