Final answer:
The angles of the triangle in the sexagesimal system are 20 degrees, 40 degrees, and 60 degrees. In the centesimal system, the angles are 11.111 grad, 22.222 grad, and 33.333 grad. In the circular system, the angles are π/9 radians, 2π/9 radians, and π/3 radians.
Step-by-step explanation:
We will find the angles of the triangle in three different systems of measurement: sexagesimal system, centesimal system, and circular system (radian).
Let the angles of the triangle be x degrees, 2x degrees, and 3x degrees.
To find the angles in the sexagesimal system, we can set up the equation x + 2x + 3x = 180, since the sum of all angles in a triangle is 180 degrees. Solving this equation gives x = 20 degrees, 2x = 40 degrees, and 3x = 60 degrees.
In the centesimal system, where angles are measured in hundredths of a right angle, we have 1 right angle = 100 grad. Therefore, x degrees = (x/180) x 100 grad. Solving for x gives x = 11.111 grad, 2x = 22.222 grad, and 3x = 33.333 grad.
In the circular system, angles are measured in radians. One full circle is equal to 2π radians. Therefore, x degrees = (x/180) x 2π radians. Solving for x gives x = π/9 radians, 2x = 2π/9 radians, and 3x = π/3 radians.
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