Angles of a line with the projection planes

Find the angles that line r (through A(2, 6, 10), direction (7, 0, 4)) makes with the PH and the PV.

Step-by-step solution

The angle with the PH is the one the line makes with its horizontal projection.
The angle with the PV is the one it makes with its vertical projection.
They are measured in true size by rotating flat the corresponding projecting plane.
If the line is parallel to a plane the angle is 0°; if perpendicular, 90°.

Result: with the PH: 29.74°; with the PV: 0°.

The two angles do not add up to 90° except in special cases; each is measured with its own projection.