In the figure, O Is the centre of the circle and NT is parallel to PR. SU = ST, ∠OPN = 54° and ∠UTS = 58°. Find
- ∠RPV
- ∠PRS
(a)
ON = OP = Radius
∠NPO = ∠PNO = 54° (Isosceles triangle, ONB)
∠POV
= 54° + 54°
= 108° (Exterior angle of a triangle)
OP = OV = Radius
∠OVP
= (180° - 108°) ÷ 2
= 72° ÷ 2
= 36°
∠RPV = 36° (Alternate angles, PR//NE)
(b)
SU = ST
∠STU = ∠SUT = 58° (Isosceles triangle STF)
∠TSU
= 180° - 58° - 58°
= 64°
∠VSR = ∠TSU = 64° (Vertically opposite angles)
∠PRS
= 180° - 64°
= 116° (Interior angles)
Answer(s): (a) 36°; (b) 116°