3). Triangle DEF. Angle D is 131 degrees. Find angle EDF and angle E.

Solution:

1. We are given a triangle DEF.
2. Angle D = 131 degrees.
3. It is indicated that angle D is formed with the horizontal line, and it is an obtuse angle (131 degrees).
4. The angle EDF is part of this angle D. However, based on the diagram, it seems that the angle marked as 131 degrees is an exterior angle or an angle formed on a straight line with the interior angle of the triangle. If we assume that the angle adjacent to 131 degrees on a straight line is the interior angle at D, then the interior angle at D would be 180 - 131 = 49 degrees. However, the diagram shows angle EDF as an acute angle within the triangle DEF.
5. There is a right angle symbol at F, meaning angle EFD = 90 degrees.
6. The sum of angles in a triangle is 180 degrees. So, angle EDF + angle E + angle EFD = 180 degrees.
7. If we assume the 131 degree angle is external to angle EDF, then the interior angle at D is 180 - 131 = 49 degrees.
8. Then, 49 degrees + angle E + 90 degrees = 180 degrees.
9. Angle E = 180 - 90 - 49 = 41 degrees.
10. Angle EDF = 49 degrees.
11. However, if angle D in the text refers to the angle EDF, then angle EDF = 131 degrees. This would make triangle DEF have two obtuse angles (131 and another one if E is also obtuse), which is impossible.
12. Let's re-examine the diagram. The 131 degree angle is shown adjacent to vertex D, outside the triangle. It appears to be an angle formed by extending one side of the triangle. If we consider the line segment DF extended to the left, and then a line segment DA such that angle ADF = 131 degrees, then the interior angle at D of triangle DEF would be 180 - 131 = 49 degrees.
13. Given angle EFD = 90 degrees.
14. In triangle DEF, the sum of angles is 180 degrees.
15. Angle EDF + Angle E + Angle EFD = 180 degrees
16. Angle EDF + Angle E + 90 degrees = 180 degrees
17. Angle EDF + Angle E = 90 degrees
18. If we assume angle EDF is the angle marked as 131 degrees, this is geometrically impossible for a triangle. The diagram shows a right angle at F. The angle labeled 131 degrees is outside the triangle at vertex D. This means the interior angle at D (angle EDF) is supplementary to 131 degrees.
19. Interior angle at D = 180° - 131° = 49°.
20. So, angle EDF = 49°.
21. Now, in right-angled triangle DEF, the sum of the two acute angles is 90°.
22. Angle EDF + Angle E = 90°.
23. 49° + Angle E = 90°.
24. Angle E = 90° - 49° = 41°.

Ответ: ∠EDF = 49°, ∠E = 41°