Answer:
The question is given below as
Concept:
The question will be solved using the linear pair theorem below
The Linear Pair Theorem states that two angles that form a linear pair are supplementary; that is, their measures add up to 180 degrees.
By applying the principle, we will have that
![\begin{gathered} \angle x+88^0=180^0 \\ collect\text{ similar terms,} \\ subtract\text{ 88 from both sides} \\ \operatorname{\angle}x+88^0-88^0=180^0-88^0 \\ \angle x=92^0 \end{gathered}]()
Hence,
The value of x= 92°
Step 2:
By applying the linear pair theorem, we will also have that
![\begin{gathered} \angle z+88^0=180^0 \\ collect\text{ similar terms, } \\ subtract\text{ 88 from both sides} \\ \operatorname{\angle}z+88^0-88=180^0-88 \\ \angle z=92^0 \end{gathered}]()
Hence,
The value of z= 92°
Step 3:
By applying the linear pair theorem also, we will have that
![\begin{gathered} \angle x+\angle y=180^0 \\ 92^0+\angle y=180^0 \\ collect\text{ similar terms,} \\ substract\text{ 92 from both sides} \\ 92^0-92^0+\operatorname{\angle}y=180^0-92^0 \\ \angle y=88^0 \end{gathered}]()
Hence,
The value of y= 88°