Question

The bisectors of angle ABC and angle BCA meet each other at O. If angle BOC= 100 degree, then angle A is ​

Answer 1

Step-by-step explanation:

ABC is a triangle in which A=60°, bisectors of angles B and C meet at point O.

In triangle ABC

60°+B+C=180°. or. B+C=120°…………….(1)

B0 is bisector of. angle B and CO is bisector of angle C . Thus

angle OBC=B/2. , angle. OCB = C/2.

In triangle OBC

angle BOC+ angle OBC. + angle OCB. =180°

angle BOC. +B/2 +C/2=180°

angle BOC = 180°- 1/2(B+C). Putting B+C=120° from eqn.(1)

angle BOC. = 180°-1/2(120°) = 180°-60°. = 120°.