Question

cancel the like term ∠y on both sides of the equation...
∠x + ∠y = 180°
∠y + ∠z = 180°
⇒ ∠x + ∠y = ∠y + ∠z

Explanation:

Step1: Start with given equations

$\angle x + \angle y = 180^\circ$
$\angle y + \angle z = 180^\circ$

Step2: Set equations equal to each other

$\angle x + \angle y = \angle y + \angle z$

Step3: Cancel $\angle y$ from both sides

$\angle x + \angle y - \angle y = \angle y + \angle z - \angle y$

Answer:

$\angle x = \angle z$