Question

find \\(qr\\).

Explanation:

🆕 New Concept Discovered: Segment Addition Postulate
The whole segment is the sum of its parts

Step 1: Identify the relationship between the segments

The points \(P\), \(Q\), and \(R\) lie on a straight line segment in that order. According to the Segment Addition Postulate, the length of the entire segment is equal to the sum of the lengths of its individual parts:

$$ PQ + QR = PR $$

Step 2: Substitute the known values

From the given image, we have:

• The total length \(PR = 89\)
• The length of the first part \(PQ = 46\)

Substitute these values into the equation:

$$ 46 + QR = 89 $$

Step 3: Solve for \(QR\)

Subtract \(46\) from both sides of the equation to find the length of \(QR\):

$$ QR = 89 - 46 $$

$$ QR = 43 $$

Answer:

43