Question

if these two figures are similar, what is the measure of the missing angle?

Explanation:

Step1: Recall the property of similar figures

Similar figures have corresponding angles equal. So, we need to find the corresponding angle in the first trapezoid to the missing angle in the second trapezoid.

Step2: Identify the angle type

Looking at the first trapezoid, the angles are \(111^\circ\), \(111^\circ\), \(69^\circ\), \(69^\circ\). The second trapezoid's missing angle should correspond to either \(111^\circ\) or \(69^\circ\). By looking at the shape (the top angles of the trapezoid), the missing angle should correspond to \(111^\circ\) (since the first trapezoid has two \(111^\circ\) angles at the top and two \(69^\circ\) at the bottom, and the second trapezoid's missing angle is at the top - like position). Alternatively, we can also calculate the sum of angles in a quadrilateral: the sum of interior angles of a quadrilateral is \((4 - 2)\times180^\circ= 360^\circ\). For the first trapezoid, sum is \(111 + 111+ 69 + 69 = 360^\circ\). For the second trapezoid, since it's similar, the angles will be the same as the first. If we assume the missing angle is a top angle (corresponding to \(111^\circ\)) or bottom (corresponding to \(69^\circ\)). From the diagram, the missing angle is at the top - right like the \(111^\circ\) angles in the first trapezoid. So the missing angle is \(111^\circ\).

Answer:

\(111\)