Question

1. given \\( \triangle l m n \cong \triangle p q r \\). set up an equation and solve for \\( x \\).

only enter the numerical value for your answer.

1. given \\( \triangle l m n \cong \triangle p q r \\). set up an equation and solve for \\( y \\).

only enter the numerical value for your answer.

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle LMN\cong\triangle PQR\), their corresponding angles are equal. \(\angle N=\angle R\).
So, \(13x - 36=42\).

Step2: Solve the equation for \(x\)

Add \(36\) to both sides of the equation: \(13x=42 + 36\), \(13x=78\).
Divide both sides by \(13\): \(x=\frac{78}{13}=6\).

Step3: Use the property of congruent triangles for \(y\)

Also, \(\angle M=\angle Q\). The sum of angles in a triangle is \(180^{\circ}\). In \(\triangle LMN\), \(\angle L=180-(112 + 42)=26^{\circ}\). Since \(\angle L=\angle P\), and \(\angle P=(2y - 6)^{\circ}\).
So, \(2y-6 = 26\).

Step4: Solve the equation for \(y\)

Add \(6\) to both sides: \(2y=26 + 6\), \(2y=32\).
Divide both sides by \(2\): \(y = 16\).

Answer:

For \(x\): \(6\)
For \(y\): \(16\)