Question

type the correct answer in each box.
complete the statement, and find the value of ( x ) in the diagram.

the quadrilateral shown is a ( square )
( x = square )

Explanation:

Step1: Identify the quadrilateral type

A kite has two distinct pairs of adjacent sides that are equal. In the given diagram, there are two distinct pairs of adjacent sides marked as equal. So the quadrilateral is a kite.

Step2: Use the property of angles in a kite

In a kite, one of the properties is that the non - vertex angles (the angles formed by the unequal sides) are equal. Also, for the angles formed by the diagonal, we can set up an equation based on the equality of angles (since in a kite, the diagonal bisects the vertex angles in some cases, and here we use the angle - equality from the side - length markings). We know that \(11x=9x + 6\) (because of the angle - equality from the side - length properties of the kite).

Step3: Solve the equation for \(x\)

Subtract \(9x\) from both sides of the equation \(11x=9x + 6\).

$$11x-9x=9x + 6-9x$$

$$2x=6$$

Divide both sides by 2:

$$x=\frac{6}{2}=3$$

Answer:

The quadrilateral shown is a kite. \(x = 3\)