Final answer:
The value of angle x at the junction of a regular hexagon and a regular octagon is 360 degrees.
Step-by-step explanation:
A regular hexagon has interior angles that measure 120 degrees each, and a regular octagon has interior angles that measure 135 degrees each.
When the hexagon and octagon are joined together, they form a shape with a total of 14 sides. To find the value of angle x at their junction, we need to subtract the sum of the interior angles of the hexagon and octagon from the sum of the interior angles of a 14-sided polygon.
The sum of interior angles of a polygon with n sides is given by the formula (n - 2) * 180 degrees. In this case, the sum of interior angles of the 14-sided polygon is (14 - 2) * 180 = 2160 degrees.
The sum of interior angles of the hexagon is 120 degrees * 6 = 720 degrees, and the sum of interior angles of the octagon is 135 degrees * 8 = 1080 degrees.
Therefore, the value of angle x at the junction of the hexagon and octagon is 2160 - (720 + 1080) = 360 degrees.