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
$\angle \text{BOD}+\angle \text{DOF}+\angle \text{FOA}=180^\circ$ (Linear pair)
$\therefore \angle \text{FOA}=\angle \text{u}=180^\circ-90^\circ-50^\circ=40^\circ$
$\angle \text{FOA}=\angle \text{x}=40^\circ$ (Vertically opposite angles)
$\angle \text{BOD}=\angle \text{z}=90^\circ$ (Vertically opposite angles)
$\angle \text{EOC}=\angle \text{y}=50^\circ$ (Vertically opposite angles)
$\therefore \angle \text{FOA}=\angle \text{u}=180^\circ-90^\circ-50^\circ=40^\circ$
$\angle \text{FOA}=\angle \text{x}=40^\circ$ (Vertically opposite angles)
$\angle \text{BOD}=\angle \text{z}=90^\circ$ (Vertically opposite angles)
$\angle \text{EOC}=\angle \text{y}=50^\circ$ (Vertically opposite angles)
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