Option C:
m(arc SR) = 100°
Solution:
∠PQT = 40°
QT and PT are radii of circle.
QT = PT
ΔPQT is an isosceles triangle.
⇒ ∠PQT = ∠QPT = 40° – – – (1)
Similarly, ΔRST is an isosceles triangle.
⇒ RST = ∠SRT – – – (2)
In ΔPQT and ΔRST,
PT ≅ TR (Radii of circle)
ST ≅ TQ (Radii of circle)
∠PQT ≅ ∠STR (by vertical theorem)
Hence ΔPQT ≅ ΔRST by SAS congruence theorem.
By corresponding parts of congruence triangles are congruent.
∠PQT = ∠RST = 40° (by (1))
∠QPT = ∠SRT = 40° (by (2))
In ΔSTR, sum of all the angles = 180°
40° + 40° + m∠PTQ = 180°
m∠STR = 180° – 80°
m∠STR = 100°
The measure of a central angle and the arc it intercepts are equal in measure.
m∠STR = m(arc SR)
m(arc SR) = 100°
Hence option C is the correct answer.
