The figure is not drawn to scale. DGJN is a parallelogram. FKM and EHL are triangles. ∠FKL = 80° and LEH = 52°. Find
- ∠EFK
- the sum of ∠ELH, ∠FBH and ∠HCK.
(a)
∠EFK
= 180° - 80°
= 100° (Interior angles, DG//NJ)
(b)
∠FBH = ∠EBC (Vertically opposite angles)
∠HCK = ∠LCB (Vertically opposite angles)
ELCB is a quadrilateral.
∠ELH + ∠LCB + ∠EBC + 52° = 360° (Sum of angles in a quadrilateral)
∠ELH + ∠LCB + ∠EBC
= 360° - 52°
= 308°
Answer(s): (a) 100°; (b) 308°