The figure is not drawn to scale. KL//NM and ML//PK. Triangles KPL and LMN are isosceles triangles. Find
- ∠j
- ∠k.
(a)
∠LMN = ∠LKP = 78° (ML//PK, LK//MN)
∠KLP
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠MLN
= 180° - 78° - 78°
= 24° (Isosceles triangle)
∠j
= 180° - 78° - 51° - 24°
= 27° (Interior angles, LK//MN)
(b)
∠k
= 180° - 28° - 27°
= 125° (Angles sum of triangle)
Answer(s): (a) 27°; (b) 125°