# The angle M of the triangle MNK is 3 times less than the angle N and 4 times less than the angle K.

September 28, 2021 | education

| **The angle M of the triangle MNK is 3 times less than the angle N and 4 times less than the angle K. Find all the corners of the triangle MNK.**

1) Suppose that the angle M of the triangle MNK is x degrees.

2) Then 3x degrees is equal to the angle N and 4x degrees is the angle K.

3) (x + 3x + 4x) degrees – is the sum of the angles of the triangle.

4) It is known that the sum of all angles of any triangle is 180 °.

Therefore, we write:

x + 3x + 4x = 180.

5) Solve the equation:

8x = 180;

x = 180: 8;

x = 22.5.

5) Hence, x = 22.5 ° – angle M.

6) Find other angles of the triangle MNK:

22.5 * 3 = 67.5 ° – angle N;

22.5 * 4 = 90 ° – angle K.

Answer: 22.5 °; 67.5 ° and 90 ° are the degree measures of the angles of the MNK triangle.

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