In the figure, O Is the centre of the circle and LS is parallel to NP. RT = RS, ∠ONL = 55° and ∠TSR = 52°. Find
- ∠PNU
- ∠NPR
(a)
OL = ON = Radius
∠LNO = ∠NLO = 55° (Isosceles triangle, OLB)
∠NOU
= 55° + 55°
= 110° (Exterior angle of a triangle)
ON = OU = Radius
∠OUN
= (180° - 110°) ÷ 2
= 70° ÷ 2
= 35°
∠PNU = 35° (Alternate angles, NP//LE)
(b)
RT = RS
∠RST = ∠RTS = 52° (Isosceles triangle RSF)
∠SRT
= 180° - 52° - 52°
= 76°
∠URP = ∠SRT = 76° (Vertically opposite angles)
∠NPR
= 180° - 76°
= 104° (Interior angles)
Answer(s): (a) 35°; (b) 104°
