Find the degree measures of the angles of the triangle MNK if the angle M is less than the angle N by 40

Find the degree measures of the angles of the triangle MNK if the angle M is less than the angle N by 40 degrees and is greater than the angle K by 10 degrees.

We denote ∠M – x °, then ∠N – (x + 40) °, and ∠K – (x – 10) °. Because the sum of the angles of the triangle is 180 °, we draw up an equation and solve it: x + (x + 40) + (x – 10) = 180; 3x = 180 – 40 + 10; 3x = 150; x = 150: 3; x = 50 ° – ∠M.

50 + 40 = 90 ° – ∠N, 50 – 10 = 40 ° – ∠K.

Answer: the angles of a triangle have degrees of 90 °, 40 °, 50 °.