Question:
In the figure given alongside, AB || CD, EF || BC, ∠BAC = 60º and ∠DHF = 50º. Find ∠GCH and ∠AGH.
Solution:
In the given figure, AB || CD and AC is the transversal.
∴ ∠ACD = ∠BAC = 60º (Pair of alternate angles)
Or ∠GCH = 60º
Now, ∠GHC = ∠DHF = 50º (Vertically opposite angles)
In ∆GCH,
∠AGH = ∠GCH + ∠GHC (Exterior angle of a triangle is equal to the sum of the two interior opposite angles)
⇒ ∠AGH = 60º + 50º = 110º