In Fig. , lines XY and MN intersect at O. If < POY = 90° and a : b = 2 : 3, find c
Line OP is perpendicular to line XY. Hence ∠POY = ∠POX = 90° ∠POX = ∠POM + ∠MOX 90° = a + b ….(1) Since a and b are in the ratio 2 : 3 that is, a = 2x and b = 3x ….(2) Substituting (2) in (1), a + b = 90° 2x + 3x = 90° 5x = 90° x = 90°/5 = 18° a = 2x = 2 × 18° a = 36° b = 3x = 3 × 18° b = 54° Also , ∠MOY= ∠MOP + ∠POY = a + 90° = 36° + 90° = 126° Lines MN and XY intersect at point O and the vertically opposite angles formed are equal. ∠XON = ∠MOY c = 126°
