Problema Solution
In quadrilateral MNOP, the degree of angle N is 40 degrees more than angle M, and 20 degrees less than that of angle O. Angle P measures 80 degrees. What is the measure of angle M?
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let
the measure of angle N be: x degrees
the degree of angle N is 40 degrees more than angle M thus the measure of angle M is: (x - 40) degrees
the degree of angle N is 20 degrees less than that of angle O thus the measure of angle O is: (x + 20) degrees
angle P measures: 80 degrees
the sum of all the angles in a quadrilateral is 360
x + (x - 40) + (x + 20) + 80 = 360
by solving we find
x = 100
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the measure of angle M is: (x - 40) degrees that is 100 - 40 = 60 degrees.