Question

c.6 angle bisectors
what is ps?
diagram: s, p, q, r with right angles at p (between pq and ps) and r (between rq and sr), ∠pqs = 51°, ∠rqs = 51°, sr = 62
ps = \square

Explanation:

Step1: Identify the Angle Bisector Theorem for Distances

Since \( QS \) is the angle bisector of \( \angle PQR \), and \( SP \perp PQ \), \( SR \perp QR \), by the Angle Bisector Theorem (the distance from a point on an angle bisector to both sides of the angle is equal), we know that \( PS = SR \).

Step2: Determine the Length of \( PS \)

We are given that \( SR = 62 \). From the Angle Bisector Theorem, \( PS = SR \). So \( PS = 62 \).

Answer:

\( 62 \)