Figure VWYX is a kite.

What is the measure of angle VXY?

(18x - 2)

720

740

106°

108°

(12x + 2)

We need to solve for the angle VXY and it is equivalent to (18x - 2) °. We all know that the total angle of the given figure is 106°, 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°.