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

Answer:

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

Explanation:

Step1: Identify the quadrilateral

The figure has two pairs of adjacent - sides equal, which is the property of a kite.

Step2: Use angle - sum property of a triangle

In the triangle formed within the kite, the sum of interior angles of a triangle is $180^{\circ}$. So, $11x+(9x + 6)=180 - 101$.

Step3: Simplify the equation

Combine like - terms: $11x+9x+6 = 79$. Then $20x+6 = 79$.

Step4: Solve for x

Subtract 6 from both sides: $20x=79 - 6=73$. Then $20x = 73$ is incorrect. Let's use the property of a kite's angles. The non - vertex angles of a kite are bisected by the diagonal. So, $11x=9x + 6$.

Step5: Solve the new equation

Subtract $9x$ from both sides: $11x-9x=9x + 6-9x$. We get $2x=6$.

Step6: Find the value of x

Divide both sides by 2: $x=\frac{6}{2}=3$.