Question

decide whether the triangles are similar. if so, determine the appropriate expression to solve for x.
the triangles are not similar, no expression for x can be found.
△abc∼△def, x = r·\frac{w}{u}
△abc∼△efd, x = r·\frac{w}{u}
△abc∼△efd, x = r·\frac{w}{z}

Explanation:

Step1: Find the third - angle of each triangle

In \(\triangle ABC\), the third - angle \(B = 180^{\circ}-(53^{\circ}+62^{\circ})=65^{\circ}\). In \(\triangle DEF\), the third - angle \(E = 180^{\circ}-(61^{\circ}+53^{\circ}) = 66^{\circ}\). Since the corresponding angles of \(\triangle ABC\) and \(\triangle DEF\) are not equal, the triangles are not similar.

Answer:

The triangles are not similar, no expression for x can be found.