In the figure, O Is the centre of the circle and LS is parallel to NP. RT = RS, ∠ONL = 57° and ∠TSR = 51°. Find
- ∠PNU
- ∠NPR
(a)
OL = ON = Radius
∠LNO = ∠NLO = 57° (Isosceles triangle, OLB)
∠NOU
= 57° + 57°
= 114° (Exterior angle of a triangle)
ON = OU = Radius
∠OUN
= (180° - 114°) ÷ 2
= 66° ÷ 2
= 33°
∠PNU = 33° (Alternate angles, NP//LE)
(b)
RT = RS
∠RST = ∠RTS = 51° (Isosceles triangle RSF)
∠SRT
= 180° - 51° - 51°
= 78°
∠URP = ∠SRT = 78° (Vertically opposite angles)
∠NPR
= 180° - 78°
= 102° (Interior angles)
Answer(s): (a) 33°; (b) 102°