We need to solve for the angle VXY and it is equivalent to (12x + 2)°. We all know that the total angle of the given figure is 360°, so by adding the angles of the four sides, we can solve for the value of x. The solution is shown below:
∠WVX + ∠VXY + ∠XYW + ∠YWV = 360°
Substituting their values, we have:
90° + (12x + 2)° + 90° + (18x -2)° = 360°
Perform addition and subtraction
90 + 12x + 2 +90 + 18x -2 = 360
30x + 180 = 360
Transpose 180 to the right side such as:
30x = 360 -180
30x = 180
Solve for x, we have:
x = 180 / 30
x = 6
Solving for the angle VXY, we have:
∠VXY = 12X + 2 = 12(6) + 2
∠VXY = 74°
The answer is 74°.