Mathematics

In figure, $$line\ XY\  ||\ line \  PQ$$ and we have $$\angle ALY=(2x-15)^o, \angle LMQ=(x+40)^o$$, find x.


SOLUTION
We have $$\angle ALY=(2x-15)^0$$ and $$\angle LMQ=(x+40)^0$$
Also, $$line\ XY\  ||\ line \  PQ$$
$$\therefore$$ $$\angle XLM$$ and $$\angle LMQ$$ are corresponding angles.
and corresponding angles on parallel lines are congruent.
$$\therefore \angle ALY=\angle LMQ$$

$$\therefore 2x-15=x+40\\$$
$$\Rightarrow 2x-x=40+15\\$$
$$\therefore x=55^0$$
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