Question

quadrilateral rstu is a parallelogram. what must be the value of x?
options: 2, 4, 5, 10

Explanation:

Step1: Recall parallelogram diagonals property

In a parallelogram, diagonals bisect each other. So, \( UV = VS \).
Given \( UV=(x - 3)\) m and \( VS=(3x - 13)\) m, we set up the equation: \( x - 3=3x - 13 \).

Step2: Solve the linear equation

Subtract \( x \) from both sides: \( - 3 = 2x - 13 \).
Add 13 to both sides: \( 10 = 2x \).
Divide both sides by 2: \( x = 5 \).

Answer:

5