Someone me! i really don’t understand anything

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

trapezoid

step-by-step explanation:

first i plotted all my points on a grid graph

i made sure all of them were in the correct quadrant

then i saw it was a trapezoid or a quadrilateral