1. It is known that a rectangular piece of paper is folded as shown in the figure, where ∠ AED' = 60, ∠ E' EB = 45, and the degree of ∠BEF is found. According to the nature of folding, we know that ∠ AED ′ and ∠ E ′ EB are equal, that is ∠ AED ′ = ∠ E ′ EB = 60. According to the properties of the rectangle, it can be concluded that ∠BEF and ∠E'EB are complementary, that is ∠BEF+∠E'EB = 180. Since ∠ e' eb = 45, we can get ∠ BEF = 180-45 = 135. So we get that the degree of ∠BEF is 135.

2. It is known that a triangular piece of paper is folded as shown in the figure, where ∠AED'= 30, ∠E'EB = 20, and the degree of ∠BEF is found. According to the nature of folding, we know that ∠ AED ′ and ∠ E ′ EB are equal, that is ∠ AED ′ = ∠ E ′ EB = 30. Because one angle of a triangle is equal to the sum of the other two angles (that is, the theorem of △ internal angle sum), we can get ∠ BEF =180-30-20 =130. So we get that the degree of ∠BEF is 130.

Common methods to solve the problem of graphic folding;

1, the application of symmetry: the shape and size of the figure will not change before and after folding, but the position will change. Therefore, we can use the nature of symmetry to solve it. For example, if a graph is symmetrical about a straight line after folding, then we can use symmetry to solve the related angles or line segments.

2. Using the theorem of triangle interior angle sum: the sum of three interior angles of triangle is equal to 180 degrees. When solving the problem of folding graphics, we can also use this theorem to solve related angles. For example, a triangle is folded in half to form an angle, and we can use the theorem of sum of internal angles of triangles to solve this angle.

3. Using the theorem of quadrilateral interior angle sum: the sum of four interior angles of a quadrilateral is equal to 360 degrees. When solving the problem of folding graphics, we can also use this theorem to solve related angles. For example, a quadrilateral is folded in half to form an angle, and we can use the theorem of sum of internal angles of quadrilateral to solve the size of this angle.

4. Using auxiliary lines: When solving the problem of folding graphics, we can also transform the problem into other geometric problems by adding auxiliary lines. For example, if a graph is folded to form an intersection, we can add an auxiliary line to connect this intersection with other points on the graph, thus transforming the problem into solving the problem of line segment length or angle.