The figure is not drawn to scale. DEGH is a parallelogram. ∠HDO is 57° and ∠GEF is 31°. DEF is an isosceles triangle and DE = EF.
- Find ∠OFE.
- Find ∠DHG.
(a)
∠EOD = 57° (Alternate angles, DH//EG)
∠EOF
= 180° - 57°
= 123° (Angles on a straight line)
∠OFE
= 180° - 123° - 31°
= 26° (Angles sum of triangle)
(b)
∠EDO = 26° (Isosceles triangle DEF)
∠DHG
= 180° - 57° - 26°
= 97° (Interior angles, DE//HG)
Answer(s): (a) 26°; (b) 97°