The sides AB and AC of a triangle are produced to D and E respectively. The bisectors of CBD and BCE meet at O. If A = 40o, find BOC.

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

B+ CBD= 180o (linear pair)

B +CBD = 90o or B + CBO = 90o
CBO = 90o -B
Similarly, BCO = 90o -C
In OBC, CBO + BCO + BOC = 180o (angle sum of a)
(90o -B) + (90o -C) + BOC = 180o
BOC = B +C +180o - 180o
BOC = (B +C)
BOC = (B +C + A) - A (adding and subtracting A)
BOC = (180o) - (40o) (A = 40o)
BOC = 70o

Answered by  | 4th Jun, 2014, 03:23: PM