Question
In the given figure, the two lines $AB$ and $CD$ intersect at a point $O$ such that $\angle\text{BOC}=125^\circ.$ Find the values of $x, y$ and $z.$ 
✓
Answer
Here, $\angle\text{AOC}$ and $\angle\text{BOC}$ from a liner pair.
$\therefore\angle\text{AOC}+\angle\text{BOC}=180^\circ$
$\Rightarrow\text{x}^\circ+125^\circ=180^\circ$
$\Rightarrow\text{x}^\circ=180^\circ-125^\circ=55^\circ$
Now, $\angle\text{AOD}=\angle\text{BOC}=125^\circ$ (Vertically opposite angles)
$\therefore\text{y}^\circ=125^\circ$
$\angle\text{BOD}=\angle\text{AOC}=55^\circ$ (Vertically opposite angles)
$\therefore\text{y}^\circ=55^\circ$ Thus, the respective values of $x, y$ and $z$ are $55, 125$ and $55.$
$\therefore\angle\text{AOC}+\angle\text{BOC}=180^\circ$
$\Rightarrow\text{x}^\circ+125^\circ=180^\circ$
$\Rightarrow\text{x}^\circ=180^\circ-125^\circ=55^\circ$
Now, $\angle\text{AOD}=\angle\text{BOC}=125^\circ$ (Vertically opposite angles)
$\therefore\text{y}^\circ=125^\circ$
$\angle\text{BOD}=\angle\text{AOC}=55^\circ$ (Vertically opposite angles)
$\therefore\text{y}^\circ=55^\circ$ Thus, the respective values of $x, y$ and $z$ are $55, 125$ and $55.$
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