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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