In the figure, O Is the centre of the circle and LS is parallel to NP. RT = RS, ∠ONL = 52° and ∠TSR = 48°. Find
- ∠PNU
- ∠NPR
(a)
OL = ON = Radius
∠LNO = ∠NLO = 52° (Isosceles triangle, OLB)
∠NOU
= 52° + 52°
= 104° (Exterior angle of a triangle)
ON = OU = Radius
∠OUN
= (180° - 104°) ÷ 2
= 76° ÷ 2
= 38°
∠PNU = 38° (Alternate angles, NP//LE)
(b)
RT = RS
∠RST = ∠RTS = 48° (Isosceles triangle RSF)
∠SRT
= 180° - 48° - 48°
= 84°
∠URP = ∠SRT = 84° (Vertically opposite angles)
∠NPR
= 180° - 84°
= 96° (Interior angles)
Answer(s): (a) 38°; (b) 96°