(a) In the diagram, O is the centre of the circle XYZ. angle ZXO=34 ° and angle XOY=146 ° . Find angle OYZ. (b) The exterior angles of a polygon are 42, 38,...

(a) In the diagram, O is the centre of the circle XYZ. angle ZXO=34 ° and angle XOY=146 ° . Find angle OYZ. 

(b) The exterior angles of a polygon are 42, 38,57, x, (x+ y)°. (2x- 15)° and (3x -y)º? If x is 7 less than y, find the values of x and y.

Answer Details

(a) ∠XYZ = 12 $\frac{1}{2}$ (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°+7x = 360° 7x 238°

x = 34

: 34 = y - 7

34 + 7 = y

41 = y