Answer
The two labeled angles measure:
$x=115$
$x-50=65$
Work Step by Step
The angle marked $x$ forms an same-side interior angle pair with the angle marked $x-50$. The same-side interior angle theorem tells us these two angles are supplementary.
$x+(x-50)=180\longrightarrow$ definition of supplementary
$2x-50=180\longrightarrow$ combine like terms
$2x=230\longrightarrow$ addition property of equality
$x=115\longrightarrow$ division property of equality
Substitute to find the measure of the other angle.
$x-50=115-50=65$
