The figure is not drawn to scale. ADFK is a parallelogram. CGJ and BEH are triangles. ∠CGH = 75° and HBE = 55°. Find
- ∠BCG
- the sum of ∠BHE, ∠CYE and ∠EZG.
(a)
∠BCG
= 180° - 75°
= 105° (Interior angles, AD//KF)
(b)
∠CYE = ∠BYZ (Vertically opposite angles)
∠EZG = ∠HZY (Vertically opposite angles)
BHZY is a quadrilateral.
∠BHE + ∠HZY + ∠BYZ + 55° = 360° (Sum of angles in a quadrilateral)
∠BHE + ∠HZY + ∠BYZ
= 360° - 55°
= 305°
Answer(s): (a) 105°; (b) 305°