Question

A, B, C and D are points on the circle, centre O. BCE is a straight line. Angle AOC= 108° and angle DCE= 60°. Calculate the values of w, x and y

Answer 1

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Answer 2

A,b,c,d are points on the circle, centre O. BCE is a straight line. Angle AOC=108° and angle DCE=60°. the values of

x°=54°

y°=60°

w°=126°

Stepwise explanation is given below:

- It is given that the angle AOC=108°

and DCE=60°......(1)

- In quadilateral AOCB

AngleAOC=2 angleABC...

( angle at the centre is equal to twice the angle at the circumfrance)

108°=2 angleABC

AngleABC=108/2=54°

- In quadilateral ABCD

Angle x+ angle w=180°

(sum of opposite angles of cyclic quadilateral is 180°)

54+ angle w=180°

Angle w=180-54=126°

- It is given that BCE is a straight line

So, angle DCE+ angle DCB=180°

60°+ angle DCB =180°

angle DCB=180-60=120°

Now, in quadilateral ABCD

- Angle x+angle y+angle w+angleDCB=360°

54°+angle y+126°+120°=360°

Angle y=360-300=60°

So, x°=54°

y°=60°

w°=126°