In the figure, O Is the centre of the circle and NT is parallel to PR. SU = ST, ∠OPN = 59° and ∠UTS = 48°. Find
- ∠RPV
- ∠PRS
(a)
ON = OP = Radius
∠NPO = ∠PNO = 59° (Isosceles triangle, ONB)
∠POV
= 59° + 59°
= 118° (Exterior angle of a triangle)
OP = OV = Radius
∠OVP
= (180° - 118°) ÷ 2
= 62° ÷ 2
= 31°
∠RPV = 31° (Alternate angles, PR//NE)
(b)
SU = ST
∠STU = ∠SUT = 48° (Isosceles triangle STF)
∠TSU
= 180° - 48° - 48°
= 84°
∠VSR = ∠TSU = 84° (Vertically opposite angles)
∠PRS
= 180° - 84°
= 96° (Interior angles)
Answer(s): (a) 31°; (b) 96°