Answer
x=15
The angles each measure 25.
Work Step by Step
Because we know that vertical equations have the same measure, we can write an equation and solve for x.
$x+10=4x-35\longrightarrow$
$x+45=4x\longrightarrow$ addition property of equality
$45=3x\longrightarrow$ subtraction property of equality
$15=x\longrightarrow$ division property of equality
Since the angles have the same measure, you can use either term and substitution to find the measures of both angles.
$x+10=15+10=25$
$4x-35=4(15)-35=60-35=25$
