Question

Find the value of z.

Answer 1

C.
`z = 82`

Explanation:

To find z, find x first:

`105 = (1)/(2)(x + 120)` (angle of intersecting chord theorem)

Solve for x

`105*2 = (1)/(2)(x + 120)*2`

`210 = x + 120`

`210 - 120 = x + 120 - 120`

`90 = x`

`x = 90`

Find z:

Full circle = 360°

Therefore,

`x + z + 68 + 120 = 360`

`90 + z + 68 + 120 = 360`

`z + 278 = 360`

`z + 278 - 278 = 360 - 278`

`z = 82`