त्रिभुज ABC का अन्तः केंद्र है। यदि, `angleACB=55^(@)` तथा `angleABC=65^(@)` हो, तब `angleBIC` ज्ञात करे?

Options

A. `130^(@)`
B. `120^(@)`
C. `140^(@)`
D. `110^(@)`

Answer

B

Explanation

According to question
Given:

`therefore angleACB+angleABC+angleBAC=180^(@)`
`angleBAC=180^(@) - 55 -65^(@)`
`angleBAC=60^(@)`
We know that
`angleBIC=90^(@) + 1/2angleA`
`angleBIC=90^(@)+1/2 xx 60`
`90+1/2xx60`
`=90+30`
`angleBIC=120^(@)`
Alternate
In `angleBIC, 1/2angleB+1/2angleC+angleBIC` = `180^(@)`
`(1)/(2)65^(@)+55^(@) + angleBIC=180^(@)`
`angleBIC=180^(@)-60^(@)=120^(@)`