Imran joins two tiles together as shown below - OCR - GCSE Maths - Question 8 - 2017 - Paper 1

To determine angle a, we first need to calculate the interior angles of the regular hexagon and the regular pentagon.

1. Interior angle of a regular hexagon:

   The formula for finding the interior angle of a regular polygon is:

   $ext{Interior Angle} = \frac{(n-2) \times 180}{n}$

   For a hexagon, where n = 6:

   $\text{Interior Angle} = \frac{(6-2) \times 180}{6} = \frac{720}{6} = 120°$

2. Interior angle of a regular pentagon:

   For a pentagon, where n = 5:

   $\text{Interior Angle} = \frac{(5-2) \times 180}{5} = \frac{540}{5} = 108°$

3. Now, calculate angle a:

   Since the angle a is supplementary to the interior angle of the pentagon, we can find it as follows:

   $a + 120° + 108° = 360°$

   Therefore:

   $a = 360° - 120° - 108°$

   Simplifying:

   $a = 360° - 228° = 132°$

Thus, angle a is shown to be 132°.