In the diagram, BCDE is a circle with centre
A. ∠BCD = (2x + 40)^\circ, ∠BAD = (5x - 35)º, ∠BED = (2y+ 10)^\circ and ∠ADC=40". Find:
(a) the values of x and y;
Attached Figure / Diagram
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a) 2x + 40 + 2y + 10 = 180^\circ...(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^\circ
y= 65 - 35
y=30^\circ
∠ABC + [2 x º35 + 40] + [5(35)-350)] + 40^\circ =360º
∠ABC + 110 + 140^\circ+ 40º = 360
∠ABC + 290^\circ = 360^\circ
∠ABC = 70^\circ
Source: Myschool Past Questions Archive (Record #65857)