∠x and ∠y are supplementary angles ∠y measures 142 what is the measure of x

Supplementary angles add up to 180

⇒ ∠x + ∠y = 180

∠x + ∠y = 180

∠x + 142 = 180

∠x = 180 - 142 = 38°

x = 38°

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: