Imagine removing the segment SP, what is the angle m∠RST?
m∠RST = 15x -10
Then, the segment SP divides the angle m∠RST in two, m∠RSP and m∠PST and we know the corresponding values (in terms of x obviously). Now, each line is a way to express the situation.
m∠RST = m∠RSP + m∠PST (by Angle Addition Postulate).
Then, with some of algebra, we obtain
7. Adjacent angles: Two angles are Adjacent when they have a common side and a common vertex (that is the corner point) and don't overlap.
Opposite angles: When two lines intersect, four angles are formed. The angles that are directly opposite to each other are called Opposite Angles
8. m∠LMN = 2 m∠LMP. But The Lienar Pair says that: Two angles that are adjacent (share a leg) and supplementary (add up to 180°). Then m∠LMN + m∠LMP = 180, so
2 m∠LMP + m∠LMP = 180, then
m∠LMP = 60