Question: 2 Work out the value of a. Explain your method. a° 105° 62° 53° Graph/shape hint: top-left, a quadrilateral-like shape with exterior angles 62°, 53°, and 105° around three vertices; the unknown interior angle a° is at the top-left vertex. 3 The diagram shows two parallel lines and two c 145° x° 43° Find the value of x. Graph/shape hint: top-right, two parallel horizontal lines with two slanted transversals meeting at a point on the right; the given angles are 145° at the top line and 43° at the bottom line, with x° at the right intersection. 4 A nonagon is a polygon with 9 sides. a) Work out the sum of the interior angles of a nonagon. b) Work out the interior angle of a regular nonagon. 5 The sum of the interior angles of a polygon is 900°. Graph/shape hint: bottom-left, text only visible for questions 4 and 5; no graph shown.

1. **Problem statement:** Find the value of the interior angle $a$ in a quadrilateral where three exterior angles are given as $62^\circ$, $53^\circ$, and $105^\circ$. 2. **Key fact:** The sum of exterior angles of any polygon is always $360^\circ$. 3. **Calculate the missing exterior angle:** $$a_{ext} = 360^\circ - (62^\circ + 53^\circ + 105^\circ)$$ $$a_{ext} = 360^\circ - 220^\circ = 140^\circ$$ 4. **Find the interior angle $a$:** Interior and exterior angles are supplementary, so $$a = 180^\circ - a_{ext} = 180^\circ - 140^\circ = 40^\circ$$ 5. **Answer:** The value of $a$ is $40^\circ$. --- **Explanation:** Exterior angles around a polygon add up to $360^\circ$. By subtracting the known exterior angles from $360^\circ$, we find the missing exterior angle. Since interior and exterior angles at the same vertex sum to $180^\circ$, subtracting the exterior angle from $180^\circ$ gives the interior angle $a$.