Question

given \\( \triangle lmn \cong \triangle qrs \\), what is the value of \\( x \\)?

choose the correct answer below.

a. 35
b. 30
c. 60
d. 45

Explanation:

Step1: Find the measure of ∠N

Use the angle - sum property of a triangle (\(180^{\circ}\) in a triangle).
\(\angle L+\angle M+\angle N = 180^{\circ}\)
\(55^{\circ}+50^{\circ}+\angle N=180^{\circ}\)
\(\angle N = 180^{\circ}-(55^{\circ}+50^{\circ})=75^{\circ}\)

Step2: Use the congruence of triangles

Since \(\triangle LMN\cong\triangle QRS\), corresponding angles are equal. So \(\angle N=\angle S\)
\(75^{\circ}=(2x - 15)^{\circ}\)

Step3: Solve for \(x\)

\(2x-15 = 75\)
Add \(15\) to both sides: \(2x=75 + 15\)
\(2x=90\)
Divide both sides by \(2\): \(x=\frac{90}{2}=45\)

Answer:

D. 45