In the figure, O Is the centre of the circle and NT is parallel to PR. SU = ST, ∠OPN = 53° and ∠UTS = 51°. Find
- ∠RPV
- ∠PRS
(a)
ON = OP = Radius
∠NPO = ∠PNO = 53° (Isosceles triangle, ONB)
∠POV
= 53° + 53°
= 106° (Exterior angle of a triangle)
OP = OV = Radius
∠OVP
= (180° - 106°) ÷ 2
= 74° ÷ 2
= 37°
∠RPV = 37° (Alternate angles, PR//NE)
(b)
SU = ST
∠STU = ∠SUT = 51° (Isosceles triangle STF)
∠TSU
= 180° - 51° - 51°
= 78°
∠VSR = ∠TSU = 78° (Vertically opposite angles)
∠PRS
= 180° - 78°
= 102° (Interior angles)
Answer(s): (a) 37°; (b) 102°
