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

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 angles formed by the unequal sides are equal. Also, for the angles formed by the two - part angle (split by the diagonal), we set up the equation based on the fact that \(11x=9x + 6\) (because in a kite, the diagonal bisects the angles between the unequal sides).
Subtract \(9x\) from both sides of the equation:
\(11x-9x=9x + 6-9x\)
\(2x=6\)
Divide both sides by 2:
\(x=\frac{6}{2}\)

Answer:

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