Question

what values of b and c make (\triangle efgcong\triangle xzy)?

Explanation:

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

Since \(\triangle EFG\cong\triangle XZY\), then \(FG = ZY\) and \(EG=XY\).
For \(FG = ZY\):
\(b + 42=45\)

Step2: Solve the equation for \(b\)

Subtract 42 from both sides of the equation \(b + 42=45\).
\(b=45 - 42\)
\(b = 3\)

Step3: For \(EG = XY\)

We have \(17=c + 15\)

Step4: Solve the equation for \(c\)

Subtract 15 from both sides of the equation \(17=c + 15\).
\(c=17-15\)
\(c = 2\)

Answer:

\(b = 3\), \(c=2\)