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 180o
A+B+C = 180o ... (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 = 60o
From (ii), we have 
120o = A+C
120o = A+2A ... From (iii)
A=40o
C=80o
Hence, the angles are 40o, 60o and 80o.

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