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: Recall angle - sum property of a quadrilateral

The sum of the interior angles of a quadrilateral is 360°.

Step2: Set up an equation

We know two angles are 101° each, and the other two angles are \(11x^{\circ}\) and \((9x + 6)^{\circ}\). So, \(101+101 + 11x+(9x + 6)=360\).

Step3: Simplify the left - hand side of the equation

Combine like terms: \((101 + 101+6)+(11x + 9x)=360\), which gives \(208+20x = 360\).

Step4: Solve for x

Subtract 208 from both sides: \(20x=360 - 208\), so \(20x = 152\). Then divide both sides by 20: \(x=\frac{152}{20}=7.6\).

Answer:

\(x = 7.6\)