In the figure, O Is the centre of the circle and PU is parallel to RS. TV = TU, ∠ORP = 55° and ∠VUT = 53°. Find
- ∠SRX
- ∠RST
(a)
OP = OR = Radius
∠PRO = ∠RPO = 55° (Isosceles triangle, OPB)
∠ROX
= 55° + 55°
= 110° (Exterior angle of a triangle)
OR = OX = Radius
∠OXR
= (180° - 110°) ÷ 2
= 70° ÷ 2
= 35°
∠SRX = 35° (Alternate angles, RS//PE)
(b)
TV = TU
∠TUV = ∠TVU = 53° (Isosceles triangle TUF)
∠UTV
= 180° - 53° - 53°
= 74°
∠XTS = ∠UTV = 74° (Vertically opposite angles)
∠RST
= 180° - 74°
= 106° (Interior angles)
Answer(s): (a) 35°; (b) 106°
