The figure is not drawn to scale. DGJN is a parallelogram. FKM and EHL are triangles. ∠FKL = 78° and LEH = 51°. Find
- ∠EFK
- the sum of ∠ELH, ∠FBH and ∠HCK.
(a)
∠EFK
= 180° - 78°
= 102° (Interior angles, DG//NJ)
(b)
∠FBH = ∠EBC (Vertically opposite angles)
∠HCK = ∠LCB (Vertically opposite angles)
ELCB is a quadrilateral.
∠ELH + ∠LCB + ∠EBC + 51° = 360° (Sum of angles in a quadrilateral)
∠ELH + ∠LCB + ∠EBC
= 360° - 51°
= 309°
Answer(s): (a) 102°; (b) 309°