Question

figure vwyx is a kite. what is the measure of angle vxy? 72° 74° 106° 108°

Explanation:

Step1: Use the property of a kite

In a kite, the sum of interior angles is \(360^{\circ}\), and \(\angle V=\angle Y = 90^{\circ}\). So, \((18x - 2)+(12x + 2)+90 + 90=360\).

Step2: Simplify the equation

Simplify the left - hand side: \(18x-2 + 12x+2+180=360\), which becomes \(30x+180 = 360\).
Subtract \(180\) from both sides: \(30x=360 - 180\), so \(30x=180\).
Divide both sides by \(30\): \(x = 6\).

Step3: Find \(\angle X\)

Substitute \(x = 6\) into \(\angle X=(12x + 2)^{\circ}\), we get \(\angle X=(12\times6+2)^{\circ}=74^{\circ}\).

Step4: Calculate \(\angle VXY\)

Since the sum of angles in a quadrilateral \(V W Y X\) is \(360^{\circ}\), and \(\angle V=\angle Y = 90^{\circ}\), \(\angle W=(18x - 2)^{\circ}=(18\times6-2)^{\circ}=106^{\circ}\).
We know that \(\angle VXY+\angle V+\angle W+\angle Y=360^{\circ}\). Let \(\angle VXY = z\), then \(z + 90+106+90=360\).
\(z=360-(90 + 106+90)=74^{\circ}\).

Answer:

\(74^{\circ}\)