Question

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

Explanation:

Step1: Use triangle angle sum property

In \(\triangle LMN\), \(\angle M = 112^{\circ}\), \(\angle N=(13x - 36)^{\circ}\). In \(\triangle PQR\), \(\angle R = 42^{\circ}\), \(\angle P=(2y - 6)^{\circ}\). Since \(\triangle LMN\cong\triangle PQR\), \(\angle M=\angle P\) (corresponding angles of congruent triangles are equal).

Step2: Set up the equation

\(2y-6 = 112\)

Step3: Solve the equation for \(y\)

Add \(6\) to both sides: \(2y=112 + 6\), so \(2y=118\).
Divide both sides by \(2\): \(y=\frac{118}{2}\)

Answer:

\(y = 59\)