The value of x in the given convex octagon is approximately 37.43
To find the value of x in the given convex octagon, we can use the fact that the sum of the interior angles of an octagon is 1080 degrees.
The given interior angles are (x+55), (3x+20), 4x, (4x-10), (6x-55), (3x+52), 3x, and (2x+30).
To find x, we need to sum up these angle measures and set it equal to 1080 degrees.
(x+55) + (3x+20) + 4x + (4x-10) + (6x-55) + (3x+52) + 3x + (2x+30) = 1080
Now, let's simplify the equation by combining like terms:
28x + 32 = 1080
Next, we isolate x by subtracting 32 from both sides:
28x = 1048
Finally, we solve for x by dividing both sides by 28:
x = 1048/28
Simplifying the division, we find:
x = 37.43
Therefore, the value of x in the given convex octagon is approximately 37.43.
The complete question could be
A convex octagon has interior angles with measures (x+55), (3x+20), 4x, (4x-10), (6x-55), (3x+52), 3x, and (2x+30). Find the value of X.