The sum of the interior angles of a pentagon is 540°. A pentagon is a polygon with five sides and five vertices.
So, in this case, you have
[tex]x\text{\degree}+135\text{\degree}+x\text{\degree}+x\text{\degree}+135\text{\degree}=540\text{\degree}[/tex]
Now, you can solve for x
[tex]\begin{gathered} x\text{\degree}+135\text{\degree}+x\text{\degree}+x\text{\degree}+135\text{\degree}=540\text{\degree} \\ \text{ Add similar terms} \\ 3x\text{\degree}+270\text{\degree}=540\text{\degree} \\ \text{ Subtract 270\degree{}from both sides of the equation} \\ 3x\text{\degree}+270\text{\degree-270\degree}=540\text{\degree-270\degree} \\ 3x\text{\degree}=270\text{\degree} \\ \text{ Divide by 3 into both sides of the equation} \\ \frac{3x\text{\degree}}{3}=\frac{270\text{\degree}}{3} \\ x=90\text{\degree} \end{gathered}[/tex]
Therefore, the angle measures in the polygon are 90°,135°,90°,90°,135°.
