Answer:
Explanation:
Since l and m are intersecting lines, they intersect at a point, say, P. Since l is parallel to p, and l intersects m at point P, angle LPQ (where Q is a point on m) is a corresponding angle to angle LPR (where R is a point on p). Therefore, angle LPQ and angle LPR are congruent. Similarly, since m is parallel to q, angle MPN (where N is a point on q) is congruent to angle MPO (where O is a point on m). Therefore, angle MPN and angle MPO are congruent.
Now, since l is parallel to p, and angle LPQ is congruent to angle LPR, we have angle LPQ + angle LPR = 180 degrees (because l and p are parallel lines, and this forms alternate interior angles). Similarly, since m is parallel to q, and angle MPN is congruent to angle MPO, we have angle MPN + angle MPO = 180 degrees (because m and q are parallel lines, and this forms alternate interior angles).
Adding these two equations, we get:
(angle LPQ + angle LPR) + (angle MPN + angle MPO) = 360 degrees
But since angles LPQ, LPR, MPN, and MPO are all angles of a quadrilateral formed by intersecting lines, their sum is equal to 360 degrees. Therefore, we can write:
360 degrees = 360 degrees
This is a true statement, and it follows from the fact that l is parallel to p, and m is parallel to q. However, this does not imply that any of the options a), b), c), or d) are necessarily true.
In fact, option d) "p is parallel to q" is not true, because if p and q were parallel, then angles LPQ and MPN would be congruent (since they are alternate interior angles), which would imply that angles LPR and MPO are also congruent (because their sum is equal to 360 degrees), which contradicts the fact that l and m intersect at point P.
Therefore, none of the options a), b), c), or d) are necessarily true, although we can derive a true statement from the given information.