Question

given (\triangle uvwcong\triangle tsr), find the values of (x), (y), and (z).

Explanation:

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

Since \(\triangle UVW\cong\triangle TSR\), then \(UV = TS\), \(VW=SR\), \(UW = TR\).
For \(UV = TS\):
\(2x - 7=53\)

Step2: Solve the equation for \(x\)

Add \(7\) to both sides of \(2x - 7=53\):
\(2x=53 + 7\)
\(2x=60\)
Divide both sides by \(2\):
\(x=\frac{60}{2}=30\)

Step3: Solve for \(y\) using \(VW = SR\)

We have \(57=5y-33\)
Add \(33\) to both sides:
\(5y=57 + 33\)
\(5y=90\)
Divide both sides by \(5\):
\(y=\frac{90}{5}=18\)

Step4: Solve for \(z\) using \(UW = TR\)

\(3z + 14=50\)
Subtract \(14\) from both sides:
\(3z=50 - 14\)
\(3z=36\)
Divide both sides by \(3\):
\(z=\frac{36}{3}=12\)

Answer:

\(x = 30\), \(y = 18\), \(z = 12\)