Given \[\begin{array}{c}{\angle \text{x}+\angle \text{y}=180^{\circ}} \\ {\angle \text{y}+\angle \text{z}=180^{\circ}}\end{array}\]We know that angles on a straight line add up to 180 degrees.So, \[\angle \text{y}=180^{\circ}-\angle \text{x} \ldots (1)\]Similarly, we know that angles around a point add up to 360 degrees.So, \[\angle \text{z}=360^{\circ}-\angle \text{y}=360^{\circ}-(180^{\circ}-\angle \text{x})=180^{\circ}+\angle \text{x} \ldots (2)\]Now, using equations (1) and (2), we can find the value of \[\angle \text{x}\].From equation (1), \[\angle \text{y}=180^{\circ}-\angle \text{x}=180^{\circ}-45^{\circ}=135^{\circ}\]From equation (2), \[\angle \text{z}=180^{\circ}+\angle \text{x}=180^{\circ}+45^{\circ}=225^{\circ}\]Hence, the value of \[\angle \text{x}\] is \[45^\circ\].Therefore, the measure of angle x is 45 degrees.