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In Fig., AM ⊥ BC and AN is the bisector of ∠A. If ∠B = 65° and ∠C = 33°, find ∠MAN.

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Best answer

Given,

AM perpendicular to BC

AN is bisector of ∠A

Therefore, ∠NAC = ∠NAB

In ΔABC

∠A + ∠B + ∠C = 180°

∠A + 65° + 33° = 180°

∠A = 180° – 98°

= 82°

∠NAC = ∠NAB = 41°(Therefore, AN is bisector of ∠A)

In ΔAMB

∠AMB + ∠MAB + ∠ABM = 180°

90° + ∠MAB + 65° = 180°

∠MAB + 155° = 180°

∠MAB = 25°

Therefore,

∠MAB + ∠MAN = ∠BAN

25° + ∠MAN = 41°

∠MAN = 41° – 25°

= 16°

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