Questions: Find the value of x that makes quadrilateral QRST a parallelogram. x=

Find the value of x that makes quadrilateral QRST a parallelogram. x=

Transcript text: * WXL-Proving a quadrikteral Day 47 id.com/math/geometry/proving-a-quadrlateralisa-parallelogram 0.7 Proving a quadrilateral is a parallelogram H89 Find the value of $x$ that makes quadrilateral $Q R S T$ a parallelogram. $x=$ Submit

Solution

Solution Steps

Step 1: Understand the Problem

We need to find the value of \( x \) that makes quadrilateral \( QRST \) a parallelogram. In a parallelogram, opposite sides are equal in length.

Step 2: Identify Opposite Sides

In the given quadrilateral \( QRST \), the opposite sides are \( QR \) and \( ST \), and \( RS \) and \( QT \).

Step 3: Set Up the Equation

Given that \( QR = 2x - 39 \) and \( ST = x \), we set these equal to each other because opposite sides in a parallelogram are equal: \[ 2x - 39 = x \]

Step 4: Solve for \( x \)

Subtract \( x \) from both sides of the equation: \[ 2x - x - 39 = 0 \] \[ x - 39 = 0 \] Add 39 to both sides: \[ x = 39 \]

Final Answer

The value of \( x \) that makes quadrilateral \( QRST \) a parallelogram is \( 39 \).

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