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Lines and Triangles — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSLines and Triangles1 Mark
Question
In the given figure, straight lines AB and CD interect at O.If $\angle\text{AOC}=\phi,\angle\text{BOC}=\theta$ and $\theta=3\phi,$
then $\phi=?$
  1. 30º
  2. 40º
  3. 45º
  4. 60º
✓

Answer

  1. 45º
Solution:
$\angle\text{AOD}=\angle\text{COB}=\theta$
$\angle\text{AOC}=\angle\text{BOD}=\phi$
Since the sum of the measures of the angles around a point is 360º,
$\angle\text{AOD}+\angle\text{COB}+\angle\text{AOC}+\angle\text{BOD}=360^\circ$
$\Rightarrow\theta+\theta+\phi+\phi=360$
$\Rightarrow2(\theta+\phi)=360$
$\Rightarrow\theta+\phi=180$
Given that $\theta=3\phi.$
So, $3\phi+\phi=180$
$\Rightarrow4\phi=180$
$\Rightarrow\phi=45$

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