1. **Problem:** Work out the size of angle $q$ in the given hexagon-like shape with angles 120°, 120°, and 60° marked. 2. **Angle fact used:** The sum of angles around a point is 360°. 3. **Step 1:** Add the known angles around the point where $q$ is located: $$120^\circ + 60^\circ + q = 180^\circ$$ This is because the angles on a straight line sum to 180°. 4. **Step 2:** Calculate $q$: $$q = 180^\circ - 120^\circ - 60^\circ$$ $$q = 0^\circ$$ This suggests $q$ is 0°, but since the problem involves a diagonal, the correct approach is to consider the interior angles of the polygon. 5. **Step 3:** For a hexagon, the sum of interior angles is: $$180^\circ \times (6 - 2) = 720^\circ$$ 6. **Step 4:** Using the given angles and the fact that the sum of angles around the vertex is 360°, the angle $q$ is: $$q = 360^\circ - 120^\circ - 120^\circ = 120^\circ$$ --- **Second problem:** Calculate the size of interior angle $c$ in a regular pentagon. 1. The formula for each interior angle of a regular polygon with $n$ sides is: $$\text{Interior angle} = \frac{180^\circ \times (n - 2)}{n}$$ 2. For a pentagon ($n=5$): $$c = \frac{180^\circ \times (5 - 2)}{5} = \frac{180^\circ \times 3}{5} = 108^\circ$$ --- **Third problem:** Match each quadrilateral with its correct mathematical name. - a) Rectangle - b) Trapezium - c) Kite - d) Parallelogram These are standard names for quadrilaterals based on their properties. **Final answers:** - $q = 120^\circ$ - $c = 108^\circ$ - Quadrilaterals matched as given.