Mathematics

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 $$u$$.


SOLUTION
According to the figure,

$$\angle EOB, \angle BOD$$ and $$\angle DOF $$ are the angles on a straight line.

thus $$\angle EOB + \angle BOD + \angle DOF =180^o$$

$$x + 90^o +50^o =180^o$$

$$x = 40^o$$

Vertically opposite angles are equal

$$z=90^o$$

$$y=50^o$$

$$x=u$$

$$\therefore z=90^o, y=50^o$$ and $$ x = u = 40^o$$

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