(a) A regular polygon of n sides is such that each interior angle is 120° greater than the exterior angle. Find : (i) the value of n ; (ii) the sum of all the interior angles. (b) A boy walks 6km from a point P to a point Q on a bearing of 065°. He then walks to a point R, a distance of 13km, on a bearing of 146°. (i) Sketch the diagram of his movement. (ii) Calculate, correct to the nearest kilometre, the distance PR.
Explanation
(a) (i) Let the exterior angle be x Let the interior angle be x + 120°. Exterior angle + Interior angle = 180° Number of sides = = (ii) Sum of interior angle = = = = (b) Note : < PQR = 65° + 34° = 99°\)
