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Lines and Triangles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsLines and Triangles2 Marks
Question
Two lines $AB$ and $CD$ intersect at $O$. If $\angle\text{AOC}=50^\circ,$ find $\angle\text{AOD},\angle\text{BOD}$ and $\angle\text{BOC}.$
 
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Answer

We know that if two lines intersect then the vertically-opposite angle are equal.
Therefore, $\angle\text{AOC}=\angle\text{BOD}=50^\circ$
Let $\angle\text{AOD}=\angle\text{BOC}=\text{x}^\circ$
Also, we know that the sum of all angles around a point is $360^\circ $.
Therefore, $\angle\text{AOC}+\angle\text{AOD}+\angle\text{BOD}+\angle\text{BOC}=360^\circ$
$\Rightarrow 50 + x + 50 + x = 360^\circ$
$\Rightarrow 2x = 260^\circ$
$\Rightarrow x = 130^\circ$
Hence, $\angle\text{AOD}=\angle\text{BOC}=130^\circ$
​​​​​​​Therefore, $\angle\text{AOD}=130^\circ,\angle\text{BOD}=50^\circ$ and $\angle\text{BOC}=130^\circ.$

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