2017 WAEC Mathematics Theory (a) PQ is a tangent to a circle RST at the point S. PRT is...

(a) PQ is a tangent to a circle RST at the point S. PRT is a straight line, < TPS = 34° and < TSQ = 65°.

(i) Illustrate the information in a diagram; (ii) find the value of : (a) < RTS ; (b) < SRP.

(b)

In the diagram, /VZ/ = /YZ/, < YXZ = 20° and < ZVY = 52°. Calculate the size of < WYZ.

(ii) (a) < RTS = 65° - 34° (exterior angles of triangle PST)

= 31°

(ii) (b) < SRP = 65° (angles in alternate segment are equal)

\(\therefore < SRP = 180° - 65° = 115°\).

(b)

If < XYZ = 128°

then < XZY = 128° + 20° = 148°

< XZV = 180° - 148° = 32°

< YVZ = < VYZ = 52° (Isoceles triangle)

< WYZ = 52° - 32° = 20°

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