In the figure, O Is the centre of the circle and LS is parallel to NP. RT = RS, ∠ONL = 59° and ∠TSR = 55°. Find
- ∠PNU
- ∠NPR
(a)
OL = ON = Radius
∠LNO = ∠NLO = 59° (Isosceles triangle, OLB)
∠NOU
= 59° + 59°
= 118° (Exterior angle of a triangle)
ON = OU = Radius
∠OUN
= (180° - 118°) ÷ 2
= 62° ÷ 2
= 31°
∠PNU = 31° (Alternate angles, NP//LE)
(b)
RT = RS
∠RST = ∠RTS = 55° (Isosceles triangle RSF)
∠SRT
= 180° - 55° - 55°
= 70°
∠URP = ∠SRT = 70° (Vertically opposite angles)
∠NPR
= 180° - 70°
= 110° (Interior angles)
Answer(s): (a) 31°; (b) 110°