1. **State the problem:** We have two congruent triangles \(\triangle RWS \cong \triangle TUV\). We need to find the values of \(x\) and \(y\) given the angles and sides. 2. **Identify corresponding parts:** Since the triangles are congruent, corresponding angles and sides are equal. - Angle \(R\) corresponds to angle \(T\). - Angle \(S\) corresponds to angle \(V\). - Side \(WS\) corresponds to side \(UV\). 3. **Use the given information:** - Angle \(R = (8x - 27)^\circ\) - Angle \(V = 29^\circ\) - Side \(VT = (3y + 7)\) 4. **Find angle \(S\):** Since \(\triangle RWS\) is right angled at \(W\), angle \(W = 90^\circ\). Sum of angles in a triangle is \(180^\circ\), so $$ (8x - 27) + 90 + S = 180 $$ Simplify: $$ S = 180 - 90 - (8x - 27) = 90 - 8x + 27 = 117 - 8x $$ 5. **Corresponding angles are equal:** Angle \(S = \) angle \(V = 29^\circ\), so $$ 117 - 8x = 29 $$ Solve for \(x\): $$ 8x = 117 - 29 = 88 $$ $$ x = \frac{88}{8} = 11 $$ 6. **Find side \(WS\):** Given \(WS = 20\) and corresponds to side \(UV\). 7. **Find side \(VT\):** Given \(VT = 3y + 7\) and corresponds to side \(RW = 15\). Set equal: $$ 3y + 7 = 15 $$ Solve for \(y\): $$ 3y = 15 - 7 = 8 $$ $$ y = \frac{8}{3} \approx 2.67 $$ **Final answers:** $$ x = 11, \quad y = \frac{8}{3}$$