Question

Tha angles of a triangle are in A.P. and the greatest angle is double the least. Find all the angles in circular measure.​

Answer 1

Let a – d, a, a + d be the three angles of the triangle that form AP. Since greatest angle is double the least. …………… (given) So, a + d = 2(a – d) or a + d = 2a – 2d or a = 3d ……(1) Again, by angle sum property, we know Sum of all the angles = 180 degrees So, (a – d) + a + (a + d) = 180° or 3a = 180° or a = 60° …… (2) From (1) and (2), we get 3d = 60° or d = 20° Now, the angles are, a – d = 60° – 20° = 40° a = 60° a + d = 60° + 20° = 80°. Therefore the required angles are 40°, 60° and 80°.

Answer 2

Let the angles be a−d,a,a+d.

& 2(a−d)=a+d,

2a−2d=a+d,

a=3d⟶(i)

a−d+a+a+d=180°,

3a=180°,

a=60°.

d=20°.

a−d,a,a+d=40,60,80.