in the figure AM |_ BC and AN is the bisector of angle A if angle ABC = 70° and angle ACB =20° . find the value of angle MAN
Answers
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
o is degree check it
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