ABSTRACT

Problem 1. State the types of quadrilateral shown in Fig. 17.6 and determine the angles marked a to l

(i) ABCD is a square The diagonals of a square bisect each of the right angles, hence

a D 90°

D 45°

(ii) EFGH is a rectangle In triangle FGH, 40° C 90° C b D 180° (angles in a triangle add up to 180°) from which, b = 50°. Also c = 40° (alternate angles between parallel lines EF and HG). (Alternatively, b and c are complementary, i.e. add up to 90°) d D 90°Cc (external angle of a triangle equals the sum of the interior opposite angles), hence

d D 90° C 40° D 130° (iii) JKLM is a rhombus

The diagonals of a rhombus bisect the interior angles and opposite internal angles are equal. Thus 6 JKM D 6 MKL D 6 JMK D 6 LMK D 30°, hence, e = 30° In triangle KLM, 30° C 6 KLMC 30° D 180° (angles in a triangle add up to 180°), hence 6 KLM D 120°. The diagonal JL bisects 6 KLM, hence

f D 120° 2

D 60°

(iv) NOPQ is a parallelogram g = 52° (since opposite interior angles of a parallelogram are equal). In triangle NOQ, gC hC 65° D 180° (angles in a triangle add up to 180°), from which,

h D 180° 65° 52° D 63° i = 65° (alternate angles between parallel lines NQ and OP). j D 52°Ci D 52°C65° D 117° (external angle of a triangle equals the sum of the interior opposite angles).