Answers:
x = 57
y = 86
z = 37
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Work Shown:
x+123 = 180 .... since x and 123 form a straight line
x = 180-123
x = 57
y = 86 since the y and 86 angles are vertical angles
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For any triangle, the three angles always add to 180. So,
x+y+z = 180
57+86+z = 180
143+z = 180
z = 180-143
z = 37
As a check,
x+y+z = 57+86+37 = 180
which confirms the value of z
