PSLE In the figure, LMNP is a parallelogram. JPL and KPN are straight lines and JK = KL. ∠JKP = 25° and ∠MNP = 57°.
- Find ∠NPL.
- Find ∠PKL.
(a)
∠NPL
= 180° - 57°
= 123° (Interior angles)
(b)
∠JPK
= ∠NPL
= 123° (Vertically opposite angles)
∠KJP
= 180° - 123° - 25°
= 32° (Angles sum of triangle)
∠KLP = ∠KJP (Isosceles triangle)
∠JKL
= 180° - 32° - 32°
= 116° (Angles sum of triangle)
∠PKL
= 116° - 25°
= 91°
Answer(s): (a) 123°; (b) 91°