Question

use the given information and the diagrams shown to determine the value of x. given: \\( \triangle lbr \cong \triangle mds \\). 9. enter your answer in the box.

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle LBR\cong\triangle MDS\), then \(\angle R=\angle S\) (corresponding angles of congruent triangles are equal).

Step2: Set up the equation

We know that \(\angle R = 2x - 1\) and \(\angle S=115^{\circ}\). So, \(2x - 1=115\).

Step3: Solve the equation for \(x\)

Add \(1\) to both sides of the equation: \(2x-1 + 1=115 + 1\), which simplifies to \(2x=116\).
Divide both sides by \(2\): \(x=\frac{116}{2}\).

Answer:

\(58\)