Question

1. given ( \triangle rws cong \triangle tuv ), find the values of ( x ) and ( y ).

Explanation:

Step1: Use the property of congruent triangles (corresponding angles are equal)

Since \(\triangle RWS\cong\triangle TUV\), then \(\angle R=\angle T = 90^{\circ}\), \(\angle S=\angle V\), and \(\angle W=\angle U\). Also, the corresponding sides are equal: \(RW = TU\), \(WS=UV\), \(RS = TV\).
For the angles: \(\angle W=(8x - 27)^{\circ}\) and \(\angle U = 29^{\circ}\). So, \(8x-27=29\).
Solve the equation \(8x-27 = 29\):
Add 27 to both sides: \(8x=29 + 27\), so \(8x=56\).
Divide both sides by 8: \(x=\frac{56}{8}=7\).

Step2: Use the property of congruent triangles (corresponding sides are equal)

For the sides: \(WS = 20\) and \(UV=5y + 7\). So, \(5y+7=20\).
Solve the equation \(5y+7 = 20\):
Subtract 7 from both sides: \(5y=20 - 7\), so \(5y=13\).
Divide both sides by 5: \(y=\frac{13}{5}=2.6\).

Answer:

\(x = 7\) and \(y=2.6\)