In the given figure, AM ⊥ BC and AN is the bisector of ∠A. If ∠ABC = 70° and ∠ACB = 20°, find ∠MAN.

Question

In the given figure, AM ⊥ BC and AN is the bisector of ∠ A. If ∠ ABC = 70 ° and ∠ ACB = 20 ° , find ∠ MAN.

Philoid · Accepted Answer

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°