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;
Explanation
(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°