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In a DeltaABC,angleA+angleB=65^(@)andang...

In a `DeltaABC,angleA+angleB=65^(@)andangleB+angleC=140^(@)`. Find the angles.

A

`angleA=40^(@),angleB=35^(@)andangleB=35^(@)andangleC=115^(@)`.

B

`angleA=40^(@),angleB=25^(@)andangleB=25^(@)andangleC=115^(@)`.

C

`angleA=40^(@),angleB=25^(@)andangleB=25^(@)andangleC=125^(@)`.

D

`angleA=50^(@),angleB=25^(@)andangleB=25^(@)andangleC=115^(@)`.

Text Solution

Verified by Experts

The correct Answer is:
B
`angleA+angleB=65^(@)andangleB+angleC=140^(@)`
`impliesangleA+angleB+angleB+angleC=(65^(@)+140^(@))`
`implies(angleA+angleB+angleC)+angleB=205^(@)`
`implies180^(@)+angleB=205^(@)[:'angleA+angleB+angleC=180^(@)]`
`impliesangleB=(205^(@)-180^(@))=25^(@)`.
`:.angleC=(140^(@)-angleB)=(140^(@)-25^(@))=115^(@)`
and `angleA=(65^(@)-angleB)=(65^(@)-25^(@))=40^(@)`.
Hence, `angleA=40^(@),angleB=25^(@)andangleB=25^(@)andangleC=115^(@)`.
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