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
$x = $

Explanation:

Step1: Identify the quadrilateral

The quadrilateral has two pairs of congruent adjacent sides and a pair of opposite congruent angles, so it is a kite.

Step2: Use kite angle property

In a kite, the angles formed by the non-congruent sides are bisected by the diagonal, so the two angles are equal:
$11x = 9x + 6$

Step3: Solve for x

Subtract $9x$ from both sides:
$11x - 9x = 6$
$2x = 6$
Divide both sides by 2:
$x = \frac{6}{2} = 3$

Answer:

The quadrilateral shown is a kite.
$x = 3$