Answer :
The measure of angle VXY is 120 degrees. Given the information provided, we have a kite VWYX with congruent sides VW and WY, congruent sides VX and XY, right angles at V and Y, angle W measuring (18x - 2) degrees, and angle X measuring (12x + 2) degrees. We need to find the measure of angle VXY.
To find the measure of angle VXY, we can use the fact that the sum of the angles in a kite is always equal to 360 degrees.
In the kite VWYX, we have:
Angle V + Angle W + Angle X + Angle Y = 360 degrees
Since angles V and Y are right angles (90 degrees), we can substitute their values:
90 degrees + (18x - 2) degrees + (12x + 2) degrees + 90 degrees = 360 degrees
Simplifying the equation:
90 degrees + 18x - 2 degrees + 12x + 2 degrees + 90 degrees = 360 degrees
Combining like terms:
120 degrees + 30x = 360 degrees
Subtracting 120 degrees from both sides:
30x = 240 degrees
Dividing both sides by 30:
x = 8 degrees
Now that we have the value of x, we can substitute it back into the expression for angle W and angle X to find their measures:
Angle W = 18x - 2 = 18(8) - 2 = 142 degrees
Angle X = 12x + 2 = 12(8) + 2 = 98 degrees
Finally, to find the measure of angle VXY, we subtract the sum of angles W and X from 360 degrees:
Angle VXY = 360 degrees - (Angle W + Angle X)
= 360 degrees - (142 degrees + 98 degrees)
= 360 degrees - 240 degrees
= 120 degrees
Therefore, the measure of angle VXY is 120 degrees.
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