Parallel lines have equal corresponding angles, so θ = α.
By shared angles, β = β.
By AA~, the triangles are similar.
12x = 4(8+x)
12x = 32 + 4x
8x = 32
x = 4
Is there enough information to prove that the triangles are similar?
Use the same method as for part (a).
Vertical angles are equal, so α = β.
Parallel lines have equal alternate interior angles,
so θ = γ.
Triangles are similar by AA~.
6x = 8(8)
6x = 64
x ≈ 10.6