The figure is not drawn to scale. DEGH is a parallelogram. ∠HDO is 59° and ∠GEF is 27°. DEF is an isosceles triangle and DE = EF.
- Find ∠OFE.
- Find ∠DHG.
(a)
∠EOD = 59° (Alternate angles, DH//EG)
∠EOF
= 180° - 59°
= 121° (Angles on a straight line)
∠OFE
= 180° - 121° - 27°
= 32° (Angles sum of triangle)
(b)
∠EDO = 32° (Isosceles triangle DEF)
∠DHG
= 180° - 59° - 32°
= 89° (Interior angles, DE//HG)
Answer(s): (a) 32°; (b) 89°