Is the dihedral angle range [0, π / 2], or is the plane angle range [0, π / 2)? Is a dihedral angle a corner? Does it have scope, What is the relationship with the plane angle range?

The range of dihedral angle
0≤θ≤π
When two half planes coincide, θ = 0, when they intersect, 0 ＜θ＜π, when they are coplanar, θ = 180

From a point in the dihedral angle to two half planes, it is proved that their angles complement the plane angles of the dihedral angle

It is proved that: let a point P in the dihedral angle m-a-n, PA ⊥ plane m at point a, PD ⊥ plane n at point D, make DC ⊥ a at point C, make ab ⊥ plane n, ∵ ab ∥ PD, point P, a, B, C and D are in the same plane, ∵ point D is on BC, ∵ ab ⊥ plane n, DC ⊥ a, ∵ AC ⊥ a, ∵ ACD are the plane angles of dihedral angle m-a-n, ∵ quadrilateral APDC, ∵ PDC = ∠ PAC = RT ∠, ∩ APD + ∧ ACD = 180 ° that is from the plane angle A point in a dihedral angle is perpendicular to two half planes, and their angles are complementary to the plane angles of the dihedral angle

There are six common methods for making plane angle of dihedral angle: 1. Definition 2. Vertical surface 3. Projective theorem 4. Three vertical line theorem
How to do it?

If the plane angle of a dihedral angle passes through a point on one surface and is perpendicular to another surface, the line is perpendicular to the intersection line of the dihedral angle
If you make a vertical line or a horizontal line, then the line is perpendicular to the other line
The angle formed by two sides starting from the midpoint is the dihedral angle formed by two adjacent faces. Let the side length of a-bcd be a, and the three sides of the triangle be 0.5A √ 3, 0.5A √ 3, a
The dihedral angle is x, cosx = (3a & sup2 / 4 + 3A & sup2 / 4-A & sup2;) / (2 * 3A & sup2 / 4) = 1 / 3

Two planes are vertical, the intersection line is a, and the angle between line B and two planes is 30 degrees. Find the angle between two lines

45 degrees, let B and two planes intersection as a, B, through a, B respectively make a vertical line, vertical foot as C, D. then through a make C ∥ a, through d make de ⊥ C, connected are right triangles, let AB = 2, we can get AE = √ 2, so cosa = √ 2 / 2, a = π / 4

Is the dihedral angle range [0, π / 2], or is the plane angle range [0, π / 2)? Is a dihedral angle a corner? Does it have scope, What is the relationship with the plane angle range?