The figure is not drawn to scale. FJLQ is a parallelogram. HMP and GKN are triangles. ∠HMN = 78° and NGK = 51°. Find
- ∠GHM
- the sum of ∠GNK, ∠HDK and ∠KEM.
(a)
∠GHM
= 180° - 78°
= 102° (Interior angles, FJ//QL)
(b)
∠HDK = ∠GDE (Vertically opposite angles)
∠KEM = ∠NED (Vertically opposite angles)
GNED is a quadrilateral.
∠GNK + ∠NED + ∠GDE + 51° = 360° (Sum of angles in a quadrilateral)
∠GNK + ∠NED + ∠GDE
= 360° - 51°
= 309°
Answer(s): (a) 102°; (b) 309°