The figure is not drawn to scale. GKMR is a parallelogram. JNQ and HLP are triangles. ∠JNP = 80° and PHL = 55°. Find
- ∠HJN
- the sum of ∠HPL, ∠JEL and ∠LFN.
(a)
∠HJN
= 180° - 80°
= 100° (Interior angles, GK//RM)
(b)
∠JEL = ∠HEF (Vertically opposite angles)
∠LFN = ∠PFE (Vertically opposite angles)
HPFE is a quadrilateral.
∠HPL + ∠PFE + ∠HEF + 55° = 360° (Sum of angles in a quadrilateral)
∠HPL + ∠PFE + ∠HEF
= 360° - 55°
= 305°
Answer(s): (a) 100°; (b) 305°