Mathematics

Find the angles x and in the figure. $$AO=OB$$


SOLUTION
Since,
$$AO=OB\Rightarrow \angle ABO=\angle x..........(1)$$

Now, $$\angle AOB=92^o$$ as it is vertically oppsite angle to $$92^o$$
 
Also, According to Sum of Opposite angle Rule 
$$x+92^o=y...................(2)$$

Also, $$\angle ABO+y=180^o\Rightarrow \angle ABO=180^o-y...................(3)$$

From (1),(2) and (3)
$$x=180^o-y\Rightarrow x=180^o-(x+92^o)\Rightarrow 2x=88^o\Rightarrow x=44^o$$

$$y=180^o-x=180^o-44^o=136^0$$
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