Question

question find the measure of \overline{dc}. answer attempt 2 out of 2

Explanation:

Step1: Identify congruent triangles

Since the two angles at \(E\) and \(C\) are equal (marked as congruent in the diagram), and the side \(ED = 22\), \(EC = 40\). By the Side - Angle - Side (SAS) congruence criterion (if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent). Here, we assume the triangles \(\triangle EDC\) and its corresponding congruent triangle (by the given angle - angle - side - like property from the diagram's angle markings) have \(ED\) corresponding to \(DC\) in a congruent relation. Wait, no, actually, if we consider the two triangles (the one with side \(ED = 22\) and the other with side \(DC\)) and the two equal angles. By the property of congruent triangles (if two angles of one triangle are equal to two angles of another triangle, the triangles are similar. But if we assume the sides adjacent to the equal angles are in proportion. Wait, no, looking at the diagram, if we use the principle of congruent triangles (the two angles are equal, and if we assume the side between them is common or in a congruent setup). Wait, actually, using the AAS (Angle - Angle - Side) congruence. If two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of another triangle, the triangles are congruent. Here, if we assume the triangles are congruent, then \(DC=ED\)

Step2: Calculate the length of \(DC\)

Since the triangles are congruent (by AAS, as two angles and a non - included side are equal), \(DC = ED\). Given \(ED = 22\), so \(DC=22\)

Answer:

\(22\)