Answer :
Let's denote the angles of the triangle as a, b, and c, with a < b < c. Given that the angles are in Arithmetic Progression (A.P.), we can express the angles as: a, a + d, and a + 2d, where d is the common difference.
Since the sum of the angles in any triangle is always 180 degrees, we have:
- a + (a + d) + (a + 2d) = 180
Simplifying this, we get:
- 3a + 3d = 180
- a + d = 60
Additionally, it's given that the greatest angle is twice the smallest angle. Therefore, we have:
- a + 2d = 2a
Solving for d, we get:
- d = a
Substituting d = a into a + d = 60, we find:
- a + a = 60
- 2a = 60
- a = 30 degrees
Consequently, the other angles are:
- a + d = 30 + 30 = 60 degrees
- a + 2d = 30 + 60 = 90 degrees
So the angles of the triangle are 30 degrees, 60 degrees, and 90 degrees. While matrices are typically used for more complex systems of equations, solving this problem relies on algebraic manipulation of the given arithmetic properties.
