Question

PQ and PR are tangents to the circle with centre O. Find:
i)angle RSQ
2. Angle RTQ
3. Angle RPQ

Answer 1

angle rst=angle trp (angles on alternate segment) i.e angle rst=40
angle qst=angle tqp (angles on the alternate segment) i.e angle qst=30
at s,
angle rsq=angle rst+angle tqp
angle rsq=70 (i)
angle roq=2(angle rsq) (angle at centre twice the angle on the remaining circimference)
i.e angle roq=140
angle roq=2(angle rtq)
i.e angle rtq=70 (ii)
angle rpq+angle roq=180 (angles b/w the tangents are supplementary)
angle rpq+140=180
angle rpq=40 (iii)