Question

, AM ⊥ BC and AN bisects ∠BAC. If ∠B=70° and ∠C=35°. Find ∠MAN.

Answer 1

∠BAN = ∠NAC = a ( bcoz AN bisects ∠BAC)

∠AMC = 90°

∠ANC = ∠BAN + ∠ABC ( Bcoz exterior angle)

∠ANC = a + 70°

∠ANB = ∠NAC + ∠ACB (Bcoz exterior angle)

∠ANB = a + 35°

∠ANC + ∠ANB = 180°

a + 70° + a + 35° = 180°

2a + 105 = 180

2a = 75°

a = 37.5°

∠ANB = a + 35 = 37.5 + 35 = 72.5°

∠MAN + ∠ANB + ∠AMC = 180° (triangle)

∠MAN + 72.5 + 90 = 180

∠MAN = 17.5°

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Answer 2

Step-by-step explanation:

angle NAC = 75°/2 = 37.5°

angle ANC = 180 - ( 37.5 + 35 ) = 107.5 °

angle ANM = 180 - 107.5 = 72.5°

angle AMN = 90°

so, angle MAN = 180 - (90 + 72.5 ) = 17.5°