In `aDeltaABC,2angleA=3angleB=6angleC,"then find "angleA,angleBandangl – InterviewSolution

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1.	In `aDeltaABC,2angleA=3angleB=6angleC,"then find "angleA,angleBandangleC`.
Answer» Let `2angleA=3angleB=6angleC=k` (say). Then, `angleA=((k)/(2))^(@),angleB=((k)/(3))^(@)andangleC=((k)/(6))^(@)` We know that the sum of the angles of a triangle is `180^(@)`. `:.angleA+angleB+angleC=180^(@)` `implies(k)/(2)+(k)/(3)+(k)/(6)=180` `implies(3k+2k+k)=(180xx6)` `implies6k=(180xx6)impliesk=180`. `:.angleA=((k)/(2))^(@)=((180)/6)^(@)=90^(@),angleB=((k)/(3))^(@)=((180)/(3))^(@)=60^(@)` and `angleC=((k)/(6))^(@)=((180)/(6))^(@)=30^(@)` Hence, `angleA=90^(@),angleB=60^(@)andangleC=30^(@)`.

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