Question

In the figure, AM I BC and AN is the bisector of
ZA. If Z ABC = 70° and ZACB = 20°, find the
value of Z MAN.​

Answer 1

Answer:

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.

Answer 2

Answer:

hope it helps you friend..............

Step-by-step explanation:

We know that the sum of all the angles in triangle ABC is 180.  

∠A + ∠B + ∠C = 180

By substituting the values

∠A + 70 + 20 = 180

On further calculation

∠A = 180 – 70– 20

By subtraction

∠A = 180– 90

=∠A= 90

We know that the sum of all the angles in triangle ABM is 180.

∠BAM + ∠ABM + ∠AMB = 180

By substituting the values

∠BAM + 70 + 90 = 180

On further calculation ∠BAM = 180 – 70– 90

By subtraction

∠BAM = 180 – 160 ∠BAM = 20

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) (90) By division ∠BAN = 45

From the figure we know that ∠MAN + ∠BAM = ∠BAN By substituting the values we get

∠MAN + 20 = 45

On further calculation ∠MAN = 45 – 20

By subtraction ∠MAN = 25

Therefore, ∠MAN = 25

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