Question

in the give figure angle ABD=66 and angle ACB= 60 if bisector of angle A meets BC at D Then find angle ADB.

Answer 1

So 87° is the answer.

Answer 2

The required angle, ∠ADB = 87°

Given:

In the given figure ∠ABD = 66° and ∠ACB = 60°

The bisector of angle A meets BC at D

To find:

Find  ∠ADB

Solution:

In given figure ABC is a triangle

As we know Sum of angles in a triangle = 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠A + 66° + 60° = 180°

⇒  ∠A = 54°

In the given figure, the bisector of angle A meets BC at D

Here the Bisector will divide ∠A into 2 equal angles

∠BAD = ∠DAC = 54/2 = 27°

⇒ ∠BAD = 27°  

If we consider ABD as a triangle

⇒ ∠ABD + ∠ADB + ∠BAD = 180°   [ sum of angles in triangle ]

⇒ 66° + ∠ADB + 27° = 180°

⇒ ∠ADB = 180° - 27° - 66°

⇒ ∠ADB = 87°  

The required angle, ∠ADB = 87°

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