Question

complete the statement, and find the value of x in the diagram.
the quadrilateral shown is a
( x = )

Explanation:

Step1: Identify the quadrilateral

The quadrilateral has two pairs of adjacent sides equal. So, it is a kite.

Step2: Use the property of a kite

In a kite, one pair of opposite angles (the angles between the unequal sides) are equal. Also, the sum of all interior angles of a quadrilateral is \(360^{\circ}\). But we can use the angle - bisecting property of the diagonal. The diagonal bisects the angles between the unequal sides. So, \(11x=9x + 6\)

Step3: Solve the equation

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. \(x = 3\)