Question

ef =
m∠f =

Explanation:

Step1: Use the property of congruent triangles

Since the two angles at \(E\) are equal (\(23^{\circ}\)) and the side opposite to one of the angles (\(18\) in) is given, we can assume the triangles are congruent (by ASA or AAS congruence if more context is considered, but from the given information of two angles and a non - included side equality in a way that for the side - angle - angle like situation). So \(EF = 18\) in.

Step2: Calculate the measure of \(\angle F\)

The sum of angles in a triangle is \(180^{\circ}\). Let \(\angle E = 23^{\circ}\), \(\angle G=23^{\circ}\). Then \(m\angle F=180^{\circ}-(23^{\circ}+ 23^{\circ})\)

$$m\angle F = 180^{\circ}-46^{\circ}=134^{\circ}$$

Answer:

\(EF = 18\) in, \(m\angle F=134^{\circ}\)