The figure is not drawn to scale. FJLQ is a parallelogram. HMP and GKN are triangles. ∠HMN = 75° and NGK = 53°. Find
- ∠GHM
- the sum of ∠GNK, ∠HDK and ∠KEM.
(a)
∠GHM
= 180° - 75°
= 105° (Interior angles, FJ//QL)
(b)
∠HDK = ∠GDE (Vertically opposite angles)
∠KEM = ∠NED (Vertically opposite angles)
GNED is a quadrilateral.
∠GNK + ∠NED + ∠GDE + 53° = 360° (Sum of angles in a quadrilateral)
∠GNK + ∠NED + ∠GDE
= 360° - 53°
= 307°
Answer(s): (a) 105°; (b) 307°