In the diagram, PQR is a tangent to the circle QST at Q. If |QT| = |ST| and ∠SQR = 68^\circ, find ∠PQT.
Attached Figure / Diagram
A
34o
B
48o
C
56o
D
68o
E
73o
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
< STQ = < SQR = 68^\circ (alternate segment)
\(\therefore\) < STQ = 68^\circ
< TQS = \(\frac{180^\circ - 68^\circ}{2}\)
= \(\frac{112}{2} = 56^\circ\)
\(\therefore\) < PQT = 180^\circ - (68^\circ + 56^\circ)
= 180^\circ - 124^\circ
= 56^\circ
Source: Myschool Past Questions Archive (Record #23205)