Question

Find the values of the variables. ​

Answer 1

x = 82

y = 98

z = 87

Explanation:

By inscribed angle theorem:

`x\degree =(1)/(2) (58\degree + 106\degree)`

`x\degree =(1)/(2)* 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