Question

In the figure given alongside, AB || CD, EF || BC, ∠BAC = 60º and ∠DHF = 50º. Find ∠GCH and ∠AGH.

Answer 1

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