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In a DeltaABC,angleA-angleB=33^(@)andang...

In a `DeltaABC,angleA-angleB=33^(@)andangleB-angleC=18^(@)`. Find the angles of the triangle.

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`angleA-angleB=33^(@)andangleB-angleC=180^(@)`
`impliesangleA=(33^(@)+angleB)=andangleC=(angleB-18^(@))." "....(i)`
We know that the sum of the angles of a triangle is `180^(@)`
`:.angleA+angleB+angleC=180^(@)`
`implies(33^(@)+angleB)+angleB+(angleB-18^(@))=180^(@)["using"(i)]`
`implies3angleB=165^(@)impliesangleB=55^(@)`
`:.angleA=(33^(@)+angleB)=(33^(@)+55^(@))=88^(@)`.
and `angleC=(angleB-18^(@))=(55^(@)-18^(@))=37^(@)`.
Hence, `angleA=88^(@),angleB=55^(@)andangleC=37^(@)`.
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