Q33 of 805 Page 257

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°


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