Question

In the given figure, AM I BC and
AN is the bisector of ZA. If
ZABC = 70° and ZAR 20°, find
Z MAN​

Answer 1

We know that the sum of all the angles in triangle ABC is 180o. ∠A + ∠B + ∠C = 180o By substituting the values ∠A + 70o + 20o = 180o On further calculation ∠A = 180o – 70o – 20o By subtraction ∠A = 180o – 90o ∠A = 90o We know that the sum of all the angles in triangle ABM is 180o. ∠BAM + ∠ABM + ∠AMB = 180o By substituting the values ∠BAM + 70o + 90o = 180o On further calculation ∠BAM = 180o – 70o – 90o By subtraction ∠BAM = 180o – 160o ∠BAM = 20o It is given that AN is the bisector of ∠A So it can be written as ∠BAN = (1/2) ∠A By substituting the values ∠BAN = (1/2) (90o) By division ∠BAN = 45o From the figure we know that ∠MAN + ∠BAM = ∠BAN By substituting the values we get ∠MAN + 20o = 45o On further calculation ∠MAN = 45o – 20o By subtraction ∠MAN = 25o Therefore, ∠MAN = 25o.

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