Question

find the values of x and y given that \\( \triangle mnp \cong \triangle tus \\).

Explanation:

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

Since \(\triangle MNP\cong\triangle TUS\), then \(NP = US\) (corresponding sides) and \(\angle M=\angle T\) (corresponding angles).
For the side - length: \(2x - y=13\). For the angle: \(2x - 50 = 24\).

Step2: Solve the equation for \(x\)

Solve \(2x - 50 = 24\).
Add \(50\) to both sides of the equation: \(2x=24 + 50\), so \(2x=74\).
Divide both sides by \(2\): \(x=\frac{74}{2}=37\).

Step3: Substitute \(x = 37\) into the equation \(2x - y=13\)

Substitute \(x = 37\) into \(2x - y=13\), we get \(2\times37-y = 13\).
Simplify the left - hand side: \(74 - y=13\).
Subtract \(74\) from both sides: \(-y=13 - 74=-61\).
Multiply both sides by \(- 1\): \(y = 61\).

Answer:

\(x = 37\) and \(y = 61\)