Question

If BO and CO are the bisectors of external angles <CBE and <BCD respectively of an equilateral ∆ABC then <BOC is equal to​

Answer 1

Answer:

Step-by-step explanation:

As BO and CO are the angle bisectors of external angles of△ABC, Then

∠1=∠2

∠4=∠3

We know, ∠A+∠ABC+∠ACB=180 ∘

…eqn(1)

And ∠ABC=180−2∠1

∠ACB=180−2∠4

Putting it in the eqn (1), we get

∠A+180−2∠1+180−2∠4=180

⇒∠1+∠4=90+ 21 ∠A…eqn(2)

Also we know from the figure, ∠BOC+∠1+∠4=180∘

∠BOC=180−∠1−∠4

From eqn (2)

∠BOC=180−90− 21 ∠A

⇒∠BOC=90 ∘ − 21 ∠A

Step-by-step explanation:

hope it will help you mate ☺️☺️☺️

Answer 2

Step-by-step explanation:

if bisectors BO and CO of angle CBE and angle BCD respectively meet at point O, then prove that angle BOC =90°-1/2 angle BAC .