In the figure shown, line ab is parallel to line cd.
part a: what is the measure of angle x? show your work. (5 points)
part b: explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)
ab and cd are parallel lines, and pq and pr are transversals which intersect ab at p and cd at q and r. angle apq is labeled as 62 degrees, angle qpr is equal to x, angle prd is equal to 115 degrees.

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?