# Q- The angles of a triangle are in AP . the greatest angle is twice the least . Find all angles of a triangle.

### Asked by arindeep.singh | 10th Jul, 2020, 06:33: PM

Expert Answer:

### Let the angles of a triangle be A, B and C such that A < B < C and A, B and C are in A.P.
Using property of triangle, sum of all internal angles is 180^{o}
A+B+C = 180^{o} ... (i)
2B = A+C ... (ii) (Since A, B & C are in A.P.)
C = 2A ... (iii) (Given)
From (i) and (ii), we get
2B+B = 180o
B = 60^{o}
From (ii), we have
120^{o} = A+C
120^{o} = A+2A ... From (iii)
A=40^{o}
C=80^{o}
Hence, the angles are 40^{o}, 60^{o} and 80^{o}.

^{o}

^{o}... (i)

^{o}

^{o}= A+C

^{o}= A+2A ... From (iii)

^{o}

^{o}

^{o}, 60

^{o}and 80

^{o}.

### Answered by Renu Varma | 12th Jul, 2020, 01:31: PM

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