we are given a polygon with 6 sides, therefore, is a hexagon. The interior angles of a hexagon always add up to 720 degrees.
Using the expression and the given angles, we can construct the following relationship:
[tex](x+80)+135+(x+50)+130+(x+75)+115=720[/tex]
Solving the operations we get:
[tex]3x+585=720[/tex]
Now we solve for "x" first by subtracting 595 to both sides:
[tex]\begin{gathered} 3x=720-585 \\ 3x=135 \end{gathered}[/tex]
Now we divide by 3:
[tex]x=\frac{135}{3}=45[/tex]
Therefore, x = 45.
Now we use the expression for angle T:
[tex]\angle T=x+50[/tex]
Replacing the value of x, we get:
[tex]\angle T=45+50=95[/tex]
Therefore, angle T is 95 degrees.
