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.
$\Rightarrow\text{x}^\circ+125^\circ=180^\circ$
$\Rightarrow\text{x}^\circ=180^\circ-125^\circ=55^\circ$
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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