Question

figure vwyx is a kite.
what is the value of x?
(18x - 2)°
(12x + 2)°
options: 3, 6, 10, 12

Explanation:

Step1: Recall properties of a kite

A kite with two right angles (at V and Y) and the other two angles (at W and X) should satisfy the property that the sum of interior angles of a quadrilateral is \(360^\circ\). Also, in this case, since angles at V and Y are right angles (\(90^\circ\) each), we can set up the equation for the sum of angles.
The sum of interior angles of a quadrilateral is \(360^\circ\), so \(90 + (18x - 2)+ 90+(12x + 2)=360\).

Step2: Simplify the equation

Combine like terms: \(90 + 90+(18x + 12x)+(- 2 + 2)=360\)
Simplify: \(180 + 30x+0 = 360\)
Which becomes \(30x+180 = 360\).

Step3: Solve for x

Subtract 180 from both sides: \(30x=360 - 180\)
\(30x = 180\)
Divide both sides by 30: \(x=\frac{180}{30}=6\)

Answer:

6