Final answer:
The value of x in the congruent triangles CAN and DCE is 31, calculated by using the angle sum property of a triangle and the congruence of corresponding angles.
Step-by-step explanation:
The question pertains to finding the value of the variable x in the context of congruent triangles.
Given that triangles CAN and DCE are congruent, the corresponding angles in both triangles must be equal.
Since we have the angle measures ABC = 61° and BCA = 57° in triangle CAN, we can find the measure of angle CAN using the fact that the sum of angles in a triangle is 180°.
The measure of angle CAN is therefore 180° - 61° - 57° = 62°.
Because triangles CAN and DCE are congruent, angle CDE, which corresponds to angle CAN, must also measure 62°.
Given CDE = 2x, we can set up the equation 2x = 62° to solve for x.
Dividing both sides by 2 gives us x = 31°.