Question

find the value of x, y and z in the figure given below

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $x = 55^{\circ}$ since the angle opposite to the $55^{\circ}$ angle and $x$ are vertical angles.

Step2: Use linear - pair property

A linear pair of angles sums to $180^{\circ}$. The angle adjacent to the $55^{\circ}$ angle and $y$ form a linear pair. So, $y+55^{\circ}=180^{\circ}$, then $y = 180^{\circ}-55^{\circ}=125^{\circ}$.

Step3: Use vertical - angle property for $z$

Since $z$ and $y$ are vertical angles, $z=y = 125^{\circ}$.

Answer:

$x = 55^{\circ}$, $y = 125^{\circ}$, $z = 125^{\circ}$