If the sum of two adjacent angles is supplementary then their outer arms in a straight line

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Sum} \mathrm{of} \mathrm{two} \mathrm{adjucent} \mathrm{angles} =180° \\ \mathrm{And} \mathrm{angle} \mathrm{of} \mathrm{straight} \mathrm{line} \mathrm{is} \mathrm{also} 180° \\ \mathrm{So} \\ \mathrm{In} \mathrm{the} \mathrm{figure} \angle \mathrm{BOC} \mathrm{and}\angle \mathrm{AOC} \mathrm{are} \mathrm{adjusent} \mathrm{angles} \\ \Rightarrow \angle \mathrm{BOC}+\angle \mathrm{AOC}=180° \left(\mathrm{given} \mathrm{in} \mathrm{the} \mathrm{problem}\right) \\ \Rightarrow \angle \mathrm{BOC}+\angle \mathrm{AOC}=180°=\mathrm{angle} \mathrm{of} \mathrm{straight} \mathrm{line} \\ \mathrm{Hence} \mathrm{their} \mathrm{outer} \mathrm{arms} \mathrm{in} \mathrm{a} \mathrm{straight} \mathrm{line}. \\ \mathrm{Hence} \mathrm{Proved} \end{gathered}$$


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