We are given the value of two angles as functions of "x"
[tex]\begin{gathered} \text{angle 1 = 2x+5;} \\ \text{angle 2 = 8x+5} \end{gathered}[/tex]These are supplentary angles, that is, their sum is 180 degrees
[tex]\text{angle 1 + angle 2 =180}^{\circ}[/tex]Replacing the values for the angles
[tex](2x+5)+(8x+5)=180[/tex]Now we solve the equation, first by adding similar terms
[tex]10x+10=180[/tex]Now we substract 10 on both sides
[tex]10x=170[/tex]Now we divide by 10 on both sides
[tex]x=\frac{170}{10}=17[/tex]The value of x is 17
