In the figure, O Is the centre of the circle and NT is parallel to PR. SU = ST, ∠OPN = 60° and ∠UTS = 49°. Find
- ∠RPV
- ∠PRS
(a)
ON = OP = Radius
∠NPO = ∠PNO = 60° (Isosceles triangle, ONB)
∠POV
= 60° + 60°
= 120° (Exterior angle of a triangle)
OP = OV = Radius
∠OVP
= (180° - 120°) ÷ 2
= 60° ÷ 2
= 30°
∠RPV = 30° (Alternate angles, PR//NE)
(b)
SU = ST
∠STU = ∠SUT = 49° (Isosceles triangle STF)
∠TSU
= 180° - 49° - 49°
= 82°
∠VSR = ∠TSU = 82° (Vertically opposite angles)
∠PRS
= 180° - 82°
= 98° (Interior angles)
Answer(s): (a) 30°; (b) 98°