In the figure, O Is the centre of the circle and LS is parallel to NP. RT = RS, ∠ONL = 56° and ∠TSR = 56°. Find
- ∠PNU
- ∠NPR
(a)
OL = ON = Radius
∠LNO = ∠NLO = 56° (Isosceles triangle, OLB)
∠NOU
= 56° + 56°
= 112° (Exterior angle of a triangle)
ON = OU = Radius
∠OUN
= (180° - 112°) ÷ 2
= 68° ÷ 2
= 34°
∠PNU = 34° (Alternate angles, NP//LE)
(b)
RT = RS
∠RST = ∠RTS = 56° (Isosceles triangle RSF)
∠SRT
= 180° - 56° - 56°
= 68°
∠URP = ∠SRT = 68° (Vertically opposite angles)
∠NPR
= 180° - 68°
= 112° (Interior angles)
Answer(s): (a) 34°; (b) 112°