Final answer:
To find the value of z in the isosceles trapezoid DEFG, set the equations for DF and EG equal to each other and solve for z. The value of z is 1.
Step-by-step explanation:
To find the value of z, we need to solve for z in the equation DF = 3z + 56 and EG = 9z + 50. Since the quadrilateral DEFG is an isosceles trapezoid, the lengths of DF and EG should be equal. So we can set 3z + 56 = 9z + 50 and solve for z.
Combine the like terms on both sides of the equation: 6z = 6. Divide both sides of the equation by 6 to solve for z: z = 1.
Therefore, the value of z is 1.