In the figure, O Is the centre of the circle and NT is parallel to PR. SU = ST, ∠OPN = 56° and ∠UTS = 54°. Find
- ∠RPV
- ∠PRS
(a)
ON = OP = Radius
∠NPO = ∠PNO = 56° (Isosceles triangle, ONB)
∠POV
= 56° + 56°
= 112° (Exterior angle of a triangle)
OP = OV = Radius
∠OVP
= (180° - 112°) ÷ 2
= 68° ÷ 2
= 34°
∠RPV = 34° (Alternate angles, PR//NE)
(b)
SU = ST
∠STU = ∠SUT = 54° (Isosceles triangle STF)
∠TSU
= 180° - 54° - 54°
= 72°
∠VSR = ∠TSU = 72° (Vertically opposite angles)
∠PRS
= 180° - 72°
= 108° (Interior angles)
Answer(s): (a) 34°; (b) 108°