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

| September 18, 2021 | education

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.

Let the degree measure of the angle M be equal to “x” degrees. Angle M is less than angle N by 40 degrees, so the degree measure of angle N is equal to “x + 40” degrees. Angle M is greater than angle K by 10 degrees, then the degree measure of angle K is equal to “x-10” degrees. Knowing that the sum of the angles of a triangle is 180 degrees, we make an equation. x + x + 40 + x – 10 = 180 3x + 30 = 180 3x = 180 – 30 3x = 150 x = 150: 3 x = 50 So the angle M is 50 degrees. The angle N is 90 degrees. x + 40 = 50 + 40 = 90 A, the angle K is 40 degrees. x – 10 = 50 – 10 = 40
Answer: 50, 90, 40 degrees.



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