`DeltaABC` की भुजा BC को बिंदु D तक बढ़ाया गया। यदि `angleACD=120^(@)` तथा `angleABC=1/2angleCAB` हे, तब `angleABC` का मान ज्ञात करे?

Options

A. `80^(@)`
B. `40^(@)`
C. `60^(@)`
D. `20^(@)`

Answer

B

Explanation

According to question, Given:

`angleACD = 120^(@)`
`(angleABC)/(angleCAB) = 1/2units`
`angleACB= 180^(@)-120^(@)`
`angleACB=180^(@)-60^(@)`
As we know that
`angleA + angleB = 120^(@)`
`angleACB = 60^(@)`
As we know that
`angleA + angleB+angleC = 180^(@)`
`angleA+angleB = 180^(@)-60^(@)`
`angleA + angleB = 40^(@)`
`angleABC = 1xx 40^(@)=40^(@)`
`angleCAB = 2xx 40^(@)=80^(@)`
`therefore angleABC=40^(@)`