Question

quadrilateral uvwx is an isosceles trapezoid, uw = 8c + 57, and vx = 5c + 81. what is the value of c?
w
v
y
u
x
c = \boxed{}

Explanation:

Step1: Use property of isosceles trapezoid

In an isosceles trapezoid, the diagonals are equal. So, \(UW = VX\).
$$8c + 57=5c + 81$$

Step2: Solve the equation for \(c\)

Subtract \(5c\) from both sides:
$$8c-5c + 57=5c-5c + 81$$
$$3c+57 = 81$$
Subtract \(57\) from both sides:
$$3c+57 - 57=81 - 57$$
$$3c=24$$
Divide both sides by \(3\):
$$\frac{3c}{3}=\frac{24}{3}$$
$$c = 8$$

Answer:

\(8\)