Question

what must the value of angle x be so that the two quadrilaterals are similar? a 60 degrees b 80 degrees c 100 degrees

Explanation:

Step1: Recall property of similar polygons

For similar polygons, corresponding angles are equal. The sum of interior - angles of a quadrilateral is 360 degrees.

Step2: Identify known angles

Let's assume we know three of the angles in one of the quadrilaterals are \(80^{\circ}\), \(100^{\circ}\), and \(120^{\circ}\).

Step3: Calculate the fourth angle

We use the formula \(A = 360-(80 + 100+120)\).
\[

$$\begin{align*} A&=360-(300)\\ A& = 60^{\circ} \end{align*}$$

\]
Since the two quadrilaterals are similar, angle \(X\) must be equal to this fourth - angle.

Answer:

A. 60 degrees