(a) PQ is a tangent to a circle RST at the point S. PRT is a straight line, < TPS = 34^\circ and < TSQ = 65^\circ.
(i) Illustrate the information in a diagram; (ii) find the value of : (a) < RTS ; (b) < SRP.
(b)
In the diagram, /VZ/ = /YZ/, < YXZ = 20^\circ and < ZVY = 52^\circ. Calculate the size of < WYZ.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(ii) (a) < RTS = 65^\circ - 34^\circ (exterior angles of triangle PST)
= 31^\circ
(ii) (b) < SRP = 65^\circ (angles in alternate segment are equal)
\(\therefore < SRP = 180^\circ - 65^\circ = 115^\circ\).
(b)
If < XYZ = 128^\circ
then < XZY = 128^\circ + 20^\circ = 148^\circ
< XZV = 180^\circ - 148^\circ = 32^\circ
< YVZ = < VYZ = 52^\circ (Isoceles triangle)
< WYZ = 52^\circ - 32^\circ = 20^\circ
Source: Myschool Past Questions Archive (Record #52358)