The figure is not drawn to scale. KL//NM and ML//PK. Triangles KPL and LMN are isosceles triangles. Find
- ∠q
- ∠r.
(a)
∠LMN = ∠LKP = 76° (ML//PK, LK//MN)
∠KLP
= (180° - 76°) ÷ 2
= 104° ÷ 2
= 52° (Isosceles triangle)
∠MLN
= 180° - 76° - 76°
= 28° (Isosceles triangle)
∠q
= 180° - 76° - 52° - 28°
= 24° (Interior angles, LK//MN)
(b)
∠r
= 180° - 29° - 24°
= 127° (Angles sum of triangle)
Answer(s): (a) 24°; (b) 127°