The figure is not drawn to scale. DGJN is a parallelogram. FKM and EHL are triangles. ∠FKL = 79° and LEH = 54°. Find
- ∠EFK
- the sum of ∠ELH, ∠FBH and ∠HCK.
(a)
∠EFK
= 180° - 79°
= 101° (Interior angles, DG//NJ)
(b)
∠FBH = ∠EBC (Vertically opposite angles)
∠HCK = ∠LCB (Vertically opposite angles)
ELCB is a quadrilateral.
∠ELH + ∠LCB + ∠EBC + 54° = 360° (Sum of angles in a quadrilateral)
∠ELH + ∠LCB + ∠EBC
= 360° - 54°
= 306°
Answer(s): (a) 101°; (b) 306°