Question

1. use the given information and the diagrams shown to determine the value of x.

given:
△lbr≅△mds

Explanation:

Step1: Recall Congruent Triangles Property

Since \( \triangle LBR \cong \triangle MDS \), corresponding angles are equal. So \( \angle R=\angle S \).

Step2: Set Up Equation

We know \( \angle S = 115^\circ \) and \( \angle R = 2x - 1 \). Thus, \( 2x - 1 = 115 \).

Step3: Solve for \( x \)

Add 1 to both sides: \( 2x = 115 + 1 = 116 \).
Divide by 2: \( x=\frac{116}{2}=46 \).

Answer:

\( x = 46 \)