In the figure, O Is the centre of the circle and NT is parallel to PR. SU = ST, ∠OPN = 58° and ∠UTS = 50°. Find
- ∠RPV
- ∠PRS
(a)
ON = OP = Radius
∠NPO = ∠PNO = 58° (Isosceles triangle, ONB)
∠POV
= 58° + 58°
= 116° (Exterior angle of a triangle)
OP = OV = Radius
∠OVP
= (180° - 116°) ÷ 2
= 64° ÷ 2
= 32°
∠RPV = 32° (Alternate angles, PR//NE)
(b)
SU = ST
∠STU = ∠SUT = 50° (Isosceles triangle STF)
∠TSU
= 180° - 50° - 50°
= 80°
∠VSR = ∠TSU = 80° (Vertically opposite angles)
∠PRS
= 180° - 80°
= 100° (Interior angles)
Answer(s): (a) 32°; (b) 100°