In the given figure, AM ⊥ BC and AN is the bisector of ∠A. If ∠ABC = 70° and ∠ACB = 20°, find ∠MAN.
In ΔABC,
∠A = 180° - 70° - 20° [Sum of all angles of a triangle = 180°]
⸫ ∠A = 90°
⸫ ∠BAN = 45° [⸪ AN is the bisector of ∠A]
In ΔABN,
∠N = 180° - 70° - 45° [Sum of all angles of a triangle = 180°]
⸫ ∠N = 65°
In ΔAMN,
∠MAN = 180° - 90° - 65° [Sum of all angles of a triangle = 180°]
⸫ ∠MAN = 25°