Two angles that fall on a line (side-by-side) add up to 180 degrees.
From the figure, we can write:
[tex](8x-23)+(5x+8)=180[/tex]
Now we can do a little algebra and solve for x:
[tex]\begin{gathered} (8x-23)+(5x+8)=180 \\ 13x-23+8=180 \\ 13x-15=180 \\ 13x=180+15 \\ 13x=195 \\ x=\frac{195}{13} \\ x=15 \end{gathered}[/tex]
Also from another pair, we can write:
[tex]z+(5x+8)=180[/tex]
We know the value of x is "15". We plug it in and solve for z:
[tex]\begin{gathered} z+5(15)+8=180 \\ z+75+8=180 \\ z+83=180 \\ z=180-83 \\ z=97 \end{gathered}[/tex]
Thus, we have our answer. They are:
[tex]x=15,z=97[/tex]
