In the diagram, BCDE is a circle with centre A. ∠BCD = (2x + 40)°, ∠BAD = (5x - 35)º, ∠BED = (2y+ 10)° and ∠ADC=40". Find: (a) the values of x and y;

Answer Details

(a) 2x + 40 + 2y + 10 = 180°...(1)

2x + 2y = 130

x + y = 65º

5x - 35 = 2(2y+ 10) ... (2)

5x - 35 = 4y +20

5x - 4y = 55

5x - 4(5-x) = 55

5x - 260 + 4x =55

9x = 315

 x = 35°

y= 65 - 35

y=30°

∠ABC + [2 x º35 + 40] + [5(35)-350)] + 40° =360º

∠ABC + 110 + 140°+ 40º = 360

∠ABC + 290° = 360°

∠ABC = 70°