The figure is not drawn to scale. FG//JH and HG//KF. Triangles FKG and GHJ are isosceles triangles. Find
- ∠p
- ∠q.
(a)
∠GHJ = ∠GFK = 78° (HG//KF, GF//HJ)
∠FGK
= (180° - 78°) ÷ 2
= 102° ÷ 2
= 51° (Isosceles triangle)
∠HGJ
= 180° - 78° - 78°
= 24° (Isosceles triangle)
∠p
= 180° - 78° - 51° - 24°
= 27° (Interior angles, GF//HJ)
(b)
∠q
= 180° - 28° - 27°
= 125° (Angles sum of triangle)
Answer(s): (a) 27°; (b) 125°