In the figure, CDEF is a parallelogram. EH, HJ and CD are straight lines. CFG is an isosceles triangle.
- Find ∠i.
- Find ∠j.
(a)
∠EHC = ∠DCJ = 65° (Corresponding angles, CD//HE)
∠HGC
= 180° - ∠EHC - ∠HCG
= 180° - 65° - 17°
= 98° (Angles sum of triangle)
∠FGC
= 180° - 98°
= 82° (Angles on a straight line)
∠GFC = ∠FGC = 82° (Isosceles triangle)
∠i
= ∠GFC
= 82° (Corresponding angles, DE//CF)
(b)
∠j
= 180° - 82° - 82°
= 16° (Isosceles triangle CFG)
Answer(s): (a) 82°; (b) 16°