Mathematics

In figure, line $$n$$ is a transversal to lines $$l$$ and $$m$$. Identify the following:
(a) angle alternate to $$\angle PQR$$, 
(b)angle corresponding to $$\angle RQF$$ and
(c) angle alternate to $$\angle PQE$$ in figure.


SOLUTION
$$(a)$$ Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines.
$$line \ n$$ is a transversal to lines $$l$$ and $$m$$
So, $$\angle ARQ$$ is relatively opposite to angle $$PQR$$ with respect to transversal $$n$$.
$$\therefore \angle ARQ$$ is angle alternate to $$\angle PQR$$

$$(b)$$ Corresponding angles are the angles which occupy the same relative position at each intersection where a straight line crosses two others.
$$line \ n$$ is a transversal that is it crosses lines $$l$$ and $$m$$
So, $$\angle BRA$$ is at relatively same position to angle $$RQF$$ with respect to transversal $$n$$.
$$\therefore \angle BRA$$ is angle alternate to $$\angle RQF$$

$$(a)$$ Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines.
$$line \ n$$ is a transversal to lines $$l$$ and $$m$$
So, $$\angle BRA$$ is relatively opposite to angle $$PQE$$ with respect to transversal $$n$$.
$$\therefore \angle BRA$$ is angle alternate to $$\angle PQE$$


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