The idea
An angle is only measured in true size. If both lines are horizontal or frontal, it is seen directly in one view; if not, you must rotate the plane that contains them flat.
Angle between two lines (direct case)
STEP 1 / 31
Two horizontal lines
r and s have the same height (4). Their vertical projections are parallel to the ground line: that means they lie in a horizontal plane.
Angle between two planes
STEP 1 / 31
The dihedral angle
It is the angle between two lines of the plane perpendicular to the intersection, one in each plane.
The missing case: line and plane
The angle between a line and a plane is the one it makes with its projection on that plane:
- If the plane is projecting, the line and its projection are seen in true length in the view where the plane looks edge-on.
- If it is not: draw the perpendicular to the plane through a point of the line; the plane formed by the line and that perpendicular cuts the given plane along the projection of the line. Rotate that plane flat and measure the angle.
- Shortcut: the angle between a line and a plane is the complement of the angle between the line and the normal to the plane.