To find the value of x+y, we will first find the sum of all the interior angles of the hexagon.The sum of the interior angles in a hexagon is always equal to 720 degrees.
All the angles in the diagram are in terms of x or y except for angle t. However, we know that the corresponding exterior angle is 30 degrees. The sum of angle t and 30 is 360. We can solve this in an algebraic equation.
t+30=360
Subtract 30 from both sides
t = 330
Now, we can solve for the values of x+y. We can set this up in another algebraic equation.
x+x+x+2y+y+30=720
Combine like terms:
3x+3y+30 = 720
Subtract 30 from both sides:
3x+3y = 690
Divide both sides by 3:
[tex] \frac{3x + 3y}{3} = \frac{690}{3} [/tex]
x+y = 230
The sum of x and y is 230.
