Q5 of 49 Page 1

The angles of a triangle are in A.P., the least being half the greatest. Find the angles.

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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