Answer:
x = 82
y = 98
z = 87
Step-by-step explanation:
By inscribed angle theorem:
[tex] x\degree =\frac{1}{2} (58\degree + 106\degree) [/tex]
[tex] x\degree =\frac{1}{2}\times 164\degree [/tex]
[tex] x\degree =82\degree [/tex]
[tex] x =82[/tex]
x° and y° are the measures of the opposite angles of a cyclic quadrilateral.
Opposite angles of a parallelogram are supplementary.
Therefore,
x° + y° = 180°
82° + y° = 180°
y° = 180° - 82°
y° = 98°
y = 98
Similarly,
93° + z° = 180°
z° = 180° - 93°
z° = 87°
z = 87
