The question asks you to find the size of angle $x$ in the diagram, where two identical octagons are joined together.

To solve this, we need to recall the formula for the interior angle of a regular polygon. For an octagon (8-sided polygon), the interior angle is calculated as:

$\text{Interior angle} = \frac{(n - 2) \times 180^\circ}{n}$ where $n$ is the number of sides. For an octagon, $n = 8$:

$\text{Interior angle of an octagon} = \frac{(8 - 2) \times 180^\circ}{8} = \frac{6 \times 180^\circ}{8} = 135^\circ$

Since the two octagons are joined together, angle $x$ is the angle formed at the junction between the two octagons. This means we need to consider the sum of the angles around that point.

To find angle $x$, we calculate the difference between the total angle around the point (which is $360^\circ$) and the sum of the two interior angles of the octagons that meet at that point:

$x = 360^\circ - 135^\circ - 135^\circ = 360^\circ - 270^\circ = 90^\circ$

Thus, the size of angle $x$ is $90^\circ$.

Would you like further explanation or have any additional questions?

Here are some related questions you might find useful:

1. How do you calculate the interior angle of a polygon with more than 8 sides?
2. What happens if two polygons with different numbers of sides are joined together?
3. How would you solve for an exterior angle of a regular polygon?
4. How do you calculate the sum of the interior angles of a polygon?
5. What is the relationship between the exterior angle and the interior angle of a regular polygon?

Tip: When two identical polygons are joined at their edges, the angles that form at the joint are key to solving the problem, especially when the interior angle of each polygon is known.