(a) In the diagram, O is the centre of the circle XYZ. angle ZXO=34 ^\circ and angle XOY=146 ^\circ . Find angle OYZ.
(b) The exterior angles of a polygon are 42, 38,57, x, (x+ y)^\circ. (2x- 15)^\circ and (3x -y)º? If x is 7 less than y, find the values of x and y.
Attached Figure / Diagram
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a) ∠XYZ = \(\frac{1}{2}\) (146) = 73º
∠OZX = 34º
∠OZY = 73 - 34
∠OYZ = ∠OZY = 39
(b) x = y - 7
42 + 38 + 57 + x + x + y + 2x - 15 + 3x - y = 360
122^\circ+7x = 360^\circ
7x = 360º - 122 = 238^\circ
7x = 238º
x = 34
: 34 = y - 7
34 + 7 = y
41 = y
Source: Myschool Past Questions Archive (Record #65869)