Two circles touch each other externally at T. RS is a direct common tangent to the two circles touching the circles at P and Q.∠TPQ=〖42〗^∘. ∠PQT (in degrees) is:

When two circles touch externally, the line joining their centers passes through the touch point T. RS is a direct common tangent touching at P and Q. The angle between tangent and radius is 90°, so ∠TPQ and ∠PQT are complementary to the angle formed by the tangent with the line of centers. Using tangent properties: ∠PQT = 90° - ∠TPQ + ∠PTQ relationship. Given ∠TPQ = 42°, and applying circle theorems about tangents from external points, we get ∠PQT = 48°.