Question
In figure, three coplanar lines intersect at a point $O$, forming angles as shown in the figure. Find the values of $x, y, z$ and $u$.
✓
Answer
$\text{z}=\angle\text{BOD}=90^\circ$ [vertically opposite angle]
$\text{y}=\angle\text{DOF}=50^\circ$ [vertically oppposite angle]
Now, $x + y + z = 180^\circ $
$\Rightarrow x + 90^\circ + 50^\circ = 180^\circ $
$\Rightarrow x = 180^\circ - 140^\circ = 40^\circ $
$\text{y}=\angle\text{DOF}=50^\circ$ [vertically oppposite angle]
Now, $x + y + z = 180^\circ $
$\Rightarrow x + 90^\circ + 50^\circ = 180^\circ $
$\Rightarrow x = 180^\circ - 140^\circ = 40^\circ $
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