Answers:
(a) x = 14
(b) line RC is parallel to line NF
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Explanation for part (a)
The angles (11x-15)° and 139° are congruent since they are vertical angles.
11x-15 = 139
11x = 139+15
11x = 154
x = 154/11
x = 14
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Explanation for part (b)
Use the x value we just found to plug into angle NGP = 9x+13
9x+13
= 9*14+13
= 139
Angle NGP = 139 and angle GDC = 139. The two alternate interior angles being congruent lets us conclude that line RC is parallel to line NF.
Or you can note that angle NGP = 139 and angle RDP = 139, and use the corresponding angles theorem to prove the lines are parallel.