Questions: Solve for x and y to make the two triangles congruent. Show your work.

Solve for \(x\) and \(y\) to make the two triangles congruent.

Find \(x\).

Since the lines AC and AE are parallel, the alternate interior angles are congruent. Thus, \(x + 9 = 71\). Subtracting 9 from both sides gives \(x = 71 - 9 = 62\).

Find \(y\).

Since the two lines are parallel, the alternate interior angles are congruent, which means \(\angle CAB = \angle EBA = 52^{\circ}\). If the triangles are congruent, the corresponding angles are equal. We can assume \(\triangle ABC \cong \triangle BAE\). Then, we have \(\angle ACB = \angle EAB\), so \(5y - 2 = 52\). Adding 2 to both sides gives \(5y = 54\). Dividing both sides by 5 gives \(y = \frac{54}{5} = 10.8\).

\(x = 62\) \(y = 10.8\)

\(x = 62\) \(y = 10.8\)