Here are the solutions for the angles:
10.2.1 Determine Q^
Step 1: Identify known angles and properties.
We are given that ST is a tangent to the circle at S, and ∠PST=42∘.
By the Tangent-Chord Theorem, the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.
So, ∠PST=∠PQS.
∠PQS=42∘
Therefore, Q^=∠PQS.
Q=42∘^
10.2.2 Determine $\hat{