Mathematics

Indicate which pairs of angles are:
Vertically opposite angles. 


ANSWER

1 & 4


SOLUTION
Considering $$\angle 1=x$$ & $$\angle 5=5x$$
$$x+5x=180^o$$
$$\Rightarrow x=30^o$$
$$\angle 1=x=30^o$$
$$\angle 5=5x=150^o$$
Being vertically opposite angles,
$$\angle 5=\angle 3+\angle 2$$
$$150^o=\angle 3+\angle 2$$
$$90^o+60^o=150^o$$
$$\angle 3=90^o$$
$$\angle 2=60^o$$
$$\angle 4+\angle 3+\angle 2=180^o$$
$$\angle 4=180-(\angle 3+\angle 2)$$
$$=180-(90+60)$$
$$=30^o$$
$$\angle 1=\angle y=30^o$$
$$\therefore 1$$ & $$4$$ are vertically opposite.
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