Question

The bisects of exterior angles at B and C of angle ABC meet at O. If angle A = x°, then angle BOC =​

Answer 1

Step-by-step explanation:

exterior angle B = angle A + interior angle C

exterior angle C = angle A + interior angle B

exterior angle (B+C) = 2x + interior angle (B+C)

exterior angle (B+C) = 2x + 180-x

exterior angle (B+C) = 180+x

dividing by 2 we get

exterior angle (B/2 + C/2) = 90+x/2

180 - angle BOC = 90 + x/2

angle BOC = 90 - x/2