Mathematics

In the diagram, PQR is a tangent to the circle QST at Q. If |QT|…

In the diagram, PQR is a tangent to the circle QST at Q. If |QT| = |ST| and ∠SQR = 68°, find ∠PQT.

  • A.
    34o
  • B.
    48o
  • C.
    56o
  • D.
    68o
  • E.
    73o
Correct Answer: Option C
Explanation

< STQ = < SQR = 68° (alternate segment)

(therefore) < STQ = 68° 

< TQS = (frac{180° – 68°}{2})

= (frac{112}{2} = 56°)

(therefore) < PQT = 180° – (68° + 56°)

= 180° – 124°

= 56°