In the MNK triangle, the angle M is 2 times, and the angle K is 6 times the angle N

In the MNK triangle, the angle M is 2 times, and the angle K is 6 times the angle N. Determine the magnitude of all the angles of the triangle MNK.

Let the magnitude of the angle LSM = X0, then, by condition, the angle NMC = 2 * X0, and the angle MKN = 6 * X0.

The sum of the interior angles of a triangle is 180.

Then X + 2 * X + 6 * X = 180.

9 * X = 180.

X = 180/9 = 20.

OLS angle = 20.

Then, the NMC angle = 2 * 20 = 40, the MCN angle = 6 * 20 = 120.

Answer: The angles of the OLS triangle are 20, 40, 120.