Question

Find the values of the variables. ​

Answer 1

Answer:

x = 82

y = 98

z = 87

Step-by-step explanation:

By inscribed angle theorem:

$x\degree =\frac{1}{2} (58\degree + 106\degree)$

$x\degree =\frac{1}{2}\times 164\degree$

$x\degree =82\degree$

$x =82$

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