In the figure, O Is the centre of the circle and PU is parallel to RS. TV = TU, ∠ORP = 54° and ∠VUT = 55°. Find
- ∠SRX
- ∠RST
(a)
OP = OR = Radius
∠PRO = ∠RPO = 54° (Isosceles triangle, OPB)
∠ROX
= 54° + 54°
= 108° (Exterior angle of a triangle)
OR = OX = Radius
∠OXR
= (180° - 108°) ÷ 2
= 72° ÷ 2
= 36°
∠SRX = 36° (Alternate angles, RS//PE)
(b)
TV = TU
∠TUV = ∠TVU = 55° (Isosceles triangle TUF)
∠UTV
= 180° - 55° - 55°
= 70°
∠XTS = ∠UTV = 70° (Vertically opposite angles)
∠RST
= 180° - 70°
= 110° (Interior angles)
Answer(s): (a) 36°; (b) 110°