Answer:
∠DEF = 250°
Step-by-step explanation:
1. This shape is a hexagon (6 sides), so the interior angles should all add to 720°. Also worth noting: the problem says the <em>obtuse</em> angle DEF; this means it's the angle INSIDE the shape, not outside.
2. Add all the known angles, then subtract from the total degrees:
50 + 96 + 144 + 42 = 332
720 - 332 = 338
3. Because BC is parallel to ED, we can subtract 180 - 42 for the value of ∠EDC, which is 138°.
4. Add all the known values and subtract from 720 for the value of ∠DEF:
50 + 96 + 144 + 42 + 138 = 470
720 - 470 = 250°
