Question

Find the measure of ∠C if ∠A = 3 2 x + 20 ∠B = 7 2 x + 20 ∠C = 5 2 x + 40 ∠D = 3 2 x + 10 A) 65° B) 76° C) 95° D) 115°

Answer 1

Answer: D) 115 deggrees

Answer 2

The sum of the angles of a quadrilateral is 360°.
$\left(\dfrac{3}{2}x+20\right)+\left(\dfrac{7}{2}x+20\right)+\left(\dfrac{5}{2}x+40\right)+\left(\dfrac{3}{2}x+10\right)=360\\\\9x+90=360\\\\x=\dfrac{270}{9}=30$

Given that x=30, the measure of ∠C is
  ∠C = (5/2)×30 +40 = 115

The appropriate choice is ...
  D) 115°