Multiple choice

I is the incentre of ∆ABC. If BIC =108°, then A = ? If three internal angle bisector of a ∆ABC, meets at a point I inside of the triangle and BIC =108°, then find the measure of A?

  1. 81°

  2. 72°

  3. 54°

  4. 36°
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In any triangle, the angle formed at the incenter by two angle bisectors is given by BIC = 90° + A/2, where A is the angle at vertex A. Setting 90° + A/2 = 108° gives A/2 = 18°, so A = 36°. The key property is that the angle at the incenter is always 90° plus half of the opposite vertex angle.

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