In the figure, O Is the centre of the circle and LS is parallel to NP. RT = RS, ∠ONL = 52° and ∠TSR = 54°. 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 = 54° (Isosceles triangle RSF)
∠SRT
= 180° - 54° - 54°
= 72°
∠URP = ∠SRT = 72° (Vertically opposite angles)
∠NPR
= 180° - 72°
= 108° (Interior angles)
Answer(s): (a) 38°; (b) 108°