Mathematics

In the adjoining figure, if $\angle COA - \angle BOC = 50^o$, find these angles.

SOLUTION
In the figure,
$\angle COA - \angle BOC=50^{o}$ ....... $(i)$ [Given]
We know that, $\angle BOC+\angle COA=180^{o}$
$\implies \angle BOC+50^{o}+\angle COA=180^{o}$
$\implies 2\angle BOC=180^{o}-50^{o}=130^{o}$
$\implies \angle BOC=65^{o}$
From $(i)$,
$\angle COA -65^{o}=50^{o}$
$\implies \angle COA=115^{o}$
Hence, $\angle BOC=65^{o}$ and $\angle COA=115^{o}$

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