If the angle between the internal bisectors of two angles ∠ B and ∠ C of a triangle ABC is 125°, then the value of ∠ A is:

If the angle between the internal bisectors of two angles…

If the angle between the internal bisectors of two angles $\angle$ B and $\angle$ C of a triangle ABC is 125°, then the value of $\angle$ A is:

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 70°

Concept Used:

The internal bisectors of a triangle meets at the incenter.

If the angle bisectors meet at point I in triangle ABC, then

$\angle$ BIC = 90° + $\angle$ A/2

Explanation:

According to the given question,

$\angle$ BIC = 125°

So, 125° = 90° + $\angle$ A/2

⇒ $\angle$ A/2 = 125° - 90°

⇒ $\angle$ A/2 = 35°

⇒ $\angle$ A = 70°

Hence the required answer is 70°.