In the figure, O Is the centre of the circle and PU is parallel to RS. TV = TU, ∠ORP = 58° and ∠VUT = 52°. Find
- ∠SRX
- ∠RST
(a)
OP = OR = Radius
∠PRO = ∠RPO = 58° (Isosceles triangle, OPB)
∠ROX
= 58° + 58°
= 116° (Exterior angle of a triangle)
OR = OX = Radius
∠OXR
= (180° - 116°) ÷ 2
= 64° ÷ 2
= 32°
∠SRX = 32° (Alternate angles, RS//PE)
(b)
TV = TU
∠TUV = ∠TVU = 52° (Isosceles triangle TUF)
∠UTV
= 180° - 52° - 52°
= 76°
∠XTS = ∠UTV = 76° (Vertically opposite angles)
∠RST
= 180° - 76°
= 104° (Interior angles)
Answer(s): (a) 32°; (b) 104°