Q. 54.3( 7 Votes )

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Answer :

As given that the angles are in A.P., we choose angles as
a-d , a , a + d a>0;d>0

Where d is the common difference of A.P.

We are also given that the least angle is half times the greatest.

So, 2 (a-d) = a + d

2a – 2d = a + d

2a – a =2d + d

a = 3d ………………..(1)

Now, we know that the sum of all the angles of a triangle is 180° .

(a-d) + a + (a + d)=180°

3a =180°

a=60°

Using equation 1, we get d = a/3 =60° /3 = 20°

The angles of the triangle are

a – d = 60° – 20° = 40°

a = 60°

a + d = 60° + 20° = 80°

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