In the diagram, AB, BC and CD are three sides of a regular polygon P - Edexcel - GCSE Maths - Question 5 - 2017 - Paper 3

The exterior angle of any polygon can be calculated using:

$ext{Exterior Angle} = 180^\circ - \text{Interior Angle}$

Thus, for the 12-sided polygon:

$\text{Exterior Angle} = 180^\circ - 150^\circ = 30^\circ$

At point B, the angles formed by the sides AB, BC, and the adjacent exterior angles must sum up to 360 degrees.

Since AB and BC are sides of polygon P, each forms an angle with the square at B. The angle from the square is 90 degrees from the interior angle at point B:

$90^\circ + 90^\circ + x + x = 360^\circ$

where x is the exterior angle of polygon P. Thus:

$x = 360^\circ - 180^\circ = 180^\circ$

Since each exterior angle contributes to a regular polygon P, and each angle equals 30 degrees as previously calculated, therefore:

$\frac{180}{x} = \frac{180}{30} = 6$

The calculation shows that polygon P has 6 sides, confirming that polygon P is a hexagon.