Question

1. consider the following figure.

find qs.
qs = 61

5b find pq.
enter your next step here

Explanation:

Step1: Recall segment addition postulate

We know that \( PR = 55 \) (from \( P \) to \( R \)) and \( QR = 31 \), \( RS = 30 \). Also, \( PR = PQ + QR \), so \( PQ = PR - QR \).

Step2: Substitute values

Given \( PR = 55 \) and \( QR = 31 \), then \( PQ = 55 - 31 \).

Step3: Calculate

\( 55 - 31 = 24 \). Also, we can verify using \( QS = 61 \) (from part 5a) and \( QS = QR + RS = 31 + 30 = 61 \) (which matches the given answer). Then, since \( PR = PQ + QR \), \( PQ = PR - QR = 55 - 31 = 24 \), or alternatively, since \( PS = PQ + QR + RS = PQ + 61 \), and also \( PS = PR + RS = 55 + 30 = 85 \), so \( PQ + 61 = 85 \), then \( PQ = 85 - 61 = 24 \).

Answer:

\( PQ = 24 \)