InterviewSolution
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InterviewSolution
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The angles of a triangle are in A.P. The greatest angle is twice the least. Find all the angles |
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Answer» Given that, the angles of a triangle are in AP. Let A, B and C are angles of a `triangle ABC.` ` :. B=(A+C)/(2)` `implies 2B= A+C " " `… (i) We know that, sum of all interior angles of a `triangle ABC=180^(@)` `A+B+C=180^(@)` `implies 2B+B=180^(@) " " ` [from Eq. (i)] `implies " " 3B=180^(@)impliesB=60^(@)` Let the greatest and least angles are A and C respectively. `A=2C " " ` [by condition] ... (ii) Now, put the values of B and A inEq. (i), we get `2xx60=2C+C` `implies120=3CimpliesC=40^(@)` Put the value of C in Eq. (ii), we get `A=2xx40^(@)implies A=80^(@)` Hence, the required angles of triangle are `80^(@), 60^(@)` and `40^(@)`. |
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