Question

Trapezoid ABCD and WXYZ are congruent trapezoids. What is the value of x?

A. x = -5
B. x = 5
C. x = 15
D. x = -15

Answer 1

Answer:

B. x=5

Step-by-step explanation:

Two shapes are congruent if you can turn one into the other by moving, rotating or flipping. So if we rotate 180 degrees, say, trapezoid WXYZ and then moving it to the left, it will match trapezoid ABCD. If so, it will be true that:

$\angle BAD=\angle XWZ \\ \\ \angle BAD=4x-7 \\ \\ \angle XWZ=2x+3 \\ \\ 4x-7=2x+3 \\ \\ Solving \ for \ x: \\ \\ 4x-2x=7+3 \\ \\ 2x=10 \\ \\ \boxed{x=5}$