In the diagram, GI is a tangent to the circle at H. If EF||GI, calculate the size of ∠EHF.

In the diagram, GI is a tangent to the circle at H. If EF||GI, calculate the size of ∠EHF.

Answer Details

∠FHI = 54° = ∠EFH (alternating angles)
∠FEH = ∠EFH (isosceles triangle)
∠EHF + ∠FEH + ∠EFH = 180° (sum of the angles in a triangle)
∠EHF = 180° - (∠FEH + ∠EFH)
∠EHF = 180° - (54° - 54°) = 180° - 108°
∠EHF = 72°