As z° and 116° are vertical angles they have the same value. So z= 116°
For finding tha value of we can use the following equation.
14x - 76 = (360 - (116*2))/2 ( Since the sum of all angles must be equal to 360°)
14x - 76 = (360 - 232)/2 (Multiplying)
14x - 76 = (128)/2 (Subtracting)
14x - 76 = 64 (Dividing)
14x = 64 + 76 (Adding 76 to both sides of the equation)
14x = 140 (Adding)
x= 140/14 (Dividing by 14 on both sides of the equation)
x = 10
The answer is x=10
z= 116°