The figure is not drawn to scale. ADFK is a parallelogram. CGJ and BEH are triangles. ∠CGH = 78° and HBE = 53°. Find
- ∠BCG
- the sum of ∠BHE, ∠CYE and ∠EZG.
(a)
∠BCG
= 180° - 78°
= 102° (Interior angles, AD//KF)
(b)
∠CYE = ∠BYZ (Vertically opposite angles)
∠EZG = ∠HZY (Vertically opposite angles)
BHZY is a quadrilateral.
∠BHE + ∠HZY + ∠BYZ + 53° = 360° (Sum of angles in a quadrilateral)
∠BHE + ∠HZY + ∠BYZ
= 360° - 53°
= 307°
Answer(s): (a) 102°; (b) 307°