In triangle ABC , AM is perpendicular to BC and AN is the bisector of angle A. Find the measure of angle MAN, when angle B = 65 degree and angle C = 30 degree.
Since ∠A + ∠B + ∠C = 180°
⇒ ∠A = 85°
Also, AN is angle bisector of ∠BAC
∴ ∠BAN = ∠NAC =
As ∠ANC is exterior angle of Δ ABN
Since BC is a straight line
⇒ ∠ANB + ∠ANC = 180°
In right ΔAMN,
∠MAN + ∠ANM + ∠AMN = 180°
⇒ ∠MAN + ∠ANB + ∠AMN = 180°