Answer
$x°=60°$
$y°=55°$
$z°=65°$
Work Step by Step
The sum of the interior angles of a triangle is $180°$
$x°+y°+z°=180°$ Equation $(1)$
An exterior angle of a triangle is equal to the sum of its interior opposite angles. So, From figure,
$2x°-5°=x°+y°$
$2x°-5°-x°=y°$
$y°=x°-5°$ Equation $(2)$
$2x°+5°=x°+z°$
$2x°+5°-x°=z°$
$z°=x°+5°$ Equation $(3)$
Substituting $y°$ and $z°$ in Equation $(1)$, we get,
$x°+y°+z°=180°$
$x°+x°-5°+x°+5°=180°$
$3x°=180°$
$x°=60°$
Substituting $x°$ in Equation $(2)$ and in Equation $(3)$,
$y°=x°-5°$
$y°=60°-5°$
$y°=55°$
$z°=60°+5°$
$z°=65°$
