In the diagram below, quadrilateral V, W, X, YVWXY is inscribed in circle ZZ. Solve for xx and yy.
Z
V
W
X
Y
101°
116°
(y -69)°
(5x -26)°
To solve for xx and yy, we need to use the properties of inscribed angles in a circle.
1. Angle V + Angle X = 180 degrees (Angle sum of a quadrilateral)
101 + (5x - 26) = 180
5x - 26 = 79
5x = 105
x = 21
2. Angle W + Angle Y = 180 degrees (Angle sum of a quadrilateral)
116 + (y - 69) = 180
y - 69 = 64
y = 133
Therefore, we have solved for x = 21 and y = 133.