Question

What is the total sum of the interior degree of this polygon?What is the value of x?What is the measure of angle T

Answer 1

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:

$(x+80)+135+(x+50)+130+(x+75)+115=720$

Solving the operations we get:

$3x+585=720$

Now we solve for "x" first by subtracting 595 to both sides:

$\begin{gathered} 3x=720-585 \\ 3x=135 \end{gathered}$

Now we divide by 3:

$x=\frac{135}{3}=45$

Therefore, x = 45.

Now we use the expression for angle T:

$\angle T=x+50$

Replacing the value of x, we get:

$\angle T=45+50=95$

Therefore, angle T is 95 degrees.