Question

these triangles are congruent. what is the length of xy? (the image shows two triangles with angle and side markings; one triangle has angles 40°, 80°, and a side of 50 cm, the other has angles 70°, 70° and a side labeled xy.)

Explanation:

Step1: Recall triangle congruence

Since the triangles are congruent, corresponding angles and sides are equal. First, find the third angle of the first triangle. The sum of angles in a triangle is \(180^\circ\). So, for the first triangle with angles \(40^\circ\) and \(80^\circ\), the third angle is \(180 - 40 - 80 = 60^\circ\).

Step2: Identify corresponding angles

In congruent triangles, corresponding angles are equal. The angle we found (\(60^\circ\)) in the first triangle should correspond to \(\angle X\) in the second triangle (by matching sides and angles, as the side lengths and angle measures suggest the correspondence). So \(\angle X = 60^\circ\).

Answer:

\(60^\circ\)