Answer:
C. [tex] z = 82 [/tex]
Step-by-step explanation:
To find z, find x first:
[tex] 105 = \frac{1}{2}(x + 120) [/tex] (angle of intersecting chord theorem)
Solve for x
[tex] 105*2 = \frac{1}{2}(x + 120)*2 [/tex]
[tex] 210 = x + 120 [/tex]
[tex] 210 - 120 = x + 120 - 120 [/tex]
[tex] 90 = x [/tex]
[tex] x = 90 [/tex]
Find z:
Full circle = 360°
Therefore,
[tex] x + z + 68 + 120 = 360 [/tex]
[tex] 90 + z + 68 + 120 = 360 [/tex]
[tex] z + 278 = 360 [/tex]
[tex] z + 278 - 278 = 360 - 278 [/tex]
[tex] z = 82 [/tex]
