The angle M of the triangle MNK is 2 times less than the angle N and 3 times less than the angle K. Find all the angles of the triangle MNK.
Let the angle NMK = X0, then, by condition, the angle MNK = 3 * X0, the angle MKN = 2 * X0.
The sum of the interior angles of the triangle is 1800, then:
X + 3 * X + 2 * X = 180.
6 * X = 180.
X = 180/6 = 30.
Then the angle NMK = 30, the angle MNK = 3 * 30 = 90, the angle MKN = 2 * 30 = 60.
Answer: The angles of the triangle are 30, 60, 90.
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