Final answer:
The measure of angle DEF in triangle DEF can be determined by subtracting the sum of the other two angles from 180 degrees, unless additional information such as side lengths is provided to use other methods like trigonometry.
Step-by-step explanation:
To calculate the measure of an angle m∆DEF in triangle DEF, you need to use the fact that the sum of the angles in any triangle is always 180 degrees. If the question provides the measurements of the other two angles in triangle DEF, then you can simply subtract their sum from 180 degrees to find the measure of angle DEF. For example, if angle D measures 50 degrees and angle E measures 60 degrees, then m∆DEF = 180 - (50 + 60) = 70 degrees.
If you don't have the measures of the other angles, and the triangle is not a special type (like an isosceles or equilateral triangle), you would need more information to find the measure of angle DEF. This additional information could be side lengths, which may allow you to use trigonometric relationships or the Law of Sines or Cosines to find the angle measure.