I'll do the first problem to get you started.
Triangle SRT is a right triangle with the 90 degree angle located at angle RST. This is because segment SR is an altitude of the triangle. Altitudes of a triangle go from a vertex to the opposite side, and they are perpendicular to the opposite side.
The acute angles of right triangle SRT add up to 90 degrees. They are complementary angles.
(angle SRT) + (angle STR) = 90
(4x-8) + (6x+13) = 90 .... substitution
10x + 5 = 90
10x + 5 - 5 = 90 - 5 .... subtract 5 from both sides
10x = 85
10x/10 = 85/10 .... divide both sides by 10
x = 8.5
Therefore the answer is choice A) x = 8.5
