Question

In the given figure AM is perpendicular BC and AN is bisector of angle A. Find the measure of angle MAN​

Answer 1

Answer:

Angle MAN=35/2=17.5 degree

Step-by-step explanation:

Let the angle A be 2x. As AN is bisector of angle A , Therefore,

∠BAN = ∠NAC = x

in ΔABC,

∠B + ∠C + ∠A = 180°

65 + 30 + ∠A = 180°

∠A = 85°

Hence, x = 85/2

in ΔABN, ∠ANC is exterior angle of ΔABN,

x + 65 = ∠ANC

85/2 + 56 = ∠ANC

∠ANC = 215/2

∴∠MNA = 180 - 215/2 = 143/2

in ΔAMN,

143/2 + 90 + ∠MAN = 180°

∠MAN = 90 - 143/2

∠MAN = 35/2

<MAN =17.5

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