PSLE In the figure, LMNP is a parallelogram. JPL and KPN are straight lines and JK = KL. ∠JKP = 32° and ∠MNP = 58°.
- Find ∠NPL.
- Find ∠PKL.
(a)
∠NPL
= 180° - 58°
= 122° (Interior angles)
(b)
∠JPK
= ∠NPL
= 122° (Vertically opposite angles)
∠KJP
= 180° - 122° - 32°
= 26° (Angles sum of triangle)
∠KLP = ∠KJP (Isosceles triangle)
∠JKL
= 180° - 26° - 26°
= 128° (Angles sum of triangle)
∠PKL
= 128° - 32°
= 96°
Answer(s): (a) 122°; (b) 96°