In the figure, $\angle AOC$ and $\angle BOC$ form a linear pair. If $a - 2b = 30^o$, find $a$ and $b$.
"
Given:
$\angle AOC$ and $\angle BOC$ form a linear pair and $a - 2b = 30^o$.
To do:
We have to find $a$ and $b$.
Solution:
We know that,
Linear pairs of angles add up to 180 degrees.
Therefore,
$a+b=180^o$......(i)
$a - 2b = 30^o$
$a=30^o+2b$
Substituting $a=30^o+2b$ in (i), we get,
$30^o+2b+b=180^o$
$3b=180^o-30^o$
$3b=150^o$
$b=50^o$
$\Rightarrow a=30^o+2(50^o)=30^o+100^o=130^o$
The values of $a$ and $b$ are $130^o$ and $50^o$ respectively.
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