Answer:
The measure of angle C is 114.672°
Step-by-step explanation:
 Given: Measure of angles as 
  ∠A = 32x + 20 
 ∠B = 72x + 20 
 ∠C = 52x + 40 
 ∠D = 32x + 10 
we have to find the measure of angle C.
Consider the given angles.
Since, there are four angles, so the figure must be a quadrilateral.
Also, we know, 
Sum of measure of angles of a quadrilateral is 360°
Thus,  ∠A  + ∠B + ∠C +  ∠D = 360°
Substitute  the values , we get,
32x + 20 + 72x + 20 + 52x + 40 + 32x + 10 =360
188x + 90 = 360  
188x = 270

Thus, Measure of angle C is   52(1.436) + 40 =114.672
Thus, The measure of angle C is 114.672°