Answer
$x°=95°$
$y°=123°$
$z°=70°$
Work Step by Step
The sum of the angles of a quadrilateral is $360°$
$x°+y°+z°+72°=360°$
$x°+y°+z°=288°$ Equation $(1)$
The angles in a linear pair are supplementary. So,
$x°+z°+15°=180°$
$x°=180°-z°-15°$
$x°=165°-z°$ Equation $(2)$
$y°+z°-13°=180°$
$y°=180°-z°+13°$
$y°=193°-z°$ Equation $(3)$
Substituting $x°$ and $y°$ in Equation $(1)$, we get,
$x°+y°+z°=288°$
$165°-z°+193°-z+z°=288°$
$358°-z°=288°$
$358°-288°=z°$
$z°=70°$
Substituting $z°$ in Equation $(2)$ and in Equation $(3)$,
$x°=165°-z°$
$x°=165°-70°$
$x°=95°$
$y°=193°-z°$
$y°=193°-70°$
$y°=123°$
