Theory question 107
Angles and Polygons(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 6 km from a point P to a point Q on a bearing of 065°. He then walks to a point R, a distance of 13 km, on a bearing of 146°. (i) Sketch the diagram of his movement. (ii) Calculate, correct to the nearest kilometer, the distance PR.
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(a) I − E = 120 and I + E = 180, so E = 30° and I = 150°.
(i) n = 360 ÷ 30 = 12.
(ii) Sum = (12 − 2) × 180° = 1800°.
(b)(i) Sketch north lines at P and Q, PQ at 065° and QR at 146°.
(ii) The bearing of P from Q is 245°, so ∠PQR = 245 − 146 = 99°.
PR2 = 62 + 132 − 2(6)(13) cos 99° = 205 + 24.4 = 229.4, PR ≈ 15.1 ≈ 15 km.
Find the angle at Q from the back bearing, then use the cosine rule.