Answer:
82 degrees
Step-by-step explanation:
1. Measure of angle BAD + ABC = 180 degrees (definition of a parallelogram). Because ABC = 71, and CAD = 27, you get BAC + 71 +27 = 180. --> BAC = 82 degrees
2. BE * 2 = BD. This means that 2(2x+2) = 5x-3. This means 4x + 4 = 5x-3, which makes x = 7. AC = 2AE, which means that 2(4x-6) = AC, which means AC is 2(28-6), which makes AC = 44.
3. Because MNPQ is isosceles, NMQ = PQM. This also means PQM +NPQ = 180. NMQ = 30 +32 = 62. This makes NPQ + 62 = 180. NPQ = 118
