The sum of the angles of a quadrilateral is 360°. [tex]\left(\dfrac{3}{2}x+20\right)+\left(\dfrac{7}{2}x+20\right)+\left(\dfrac{5}{2}x+40\right)+\left(\dfrac{3}{2}x+10\right)=360\\\\9x+90=360\\\\x=\dfrac{270}{9}=30[/tex]
Given that x=30, the measure of ∠C is ∠C = (5/2)×30 +40 = 115
