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

Question

Accepted Answer

# Explanation:
## Step1: Use the property of congruent triangles
Since $\triangle LMN\cong\triangle PQR$, their corresponding angles are equal.
## Step2: Set up the equation for angle $N$ and $R$
We know that $\angle N=\angle R$. So $13x - 36=42$.
$$
\begin{align*}
13x&=42 + 36\
13x&=78\
x&=6
\end{align*}
$$
## Step3: Use the angle - sum property of a triangle
In $\triangle LMN$, $\angle L+\angle M+\angle N = 180^{\circ}$. In $\triangle PQR$, $\angle P+\angle Q+\angle R=180^{\circ}$. Also, $\angle M=\angle Q$ (corresponding angles of congruent triangles).
We know $\angle M = 112^{\circ}$, $\angle R = 42^{\circ}$. In $\triangle PQR$, $\angle P=(2y - 6)^{\circ}$, $\angle Q = 112^{\circ}$, $\angle R=42^{\circ}$
Using $\angle P+\angle Q+\angle R = 180^{\circ}$
$$
\begin{align*}
(2y-6)+112 + 42&=180\
2y-6+154&=180\
2y+148&=180\
2y&=180 - 148\
2y&=32\
y&=16
\end{align*}
$$

# Answer:
$y = 16$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the property of congruent triangles

Step2: Set up the equation for angle \(N\) and \(R\)

Step3: Use the angle - sum property of a triangle

Answer: