Angles in inclined planes: When an angle lies in a plane inclined to the plane of projection, will its projected measure appear larger or smaller than the true angle depending on orientation?

Introduction / Context:
Apparent (projected) angles often differ from true angles when the containing plane is not parallel to the projection plane. Mastering this concept helps in reading complex intersections, tapers, and chamfers on inclined faces.

Given Data / Assumptions:

• The angle lies entirely within a plane inclined to the projection plane.
• We are taking a principal orthographic view (not an auxiliary true-shape view).
• No perspective projection—strictly parallel projection.

Concept / Approach:
An angle’s apparent magnitude is governed by the foreshortening of its sides under projection. If the plane is inclined, the edge directions experience different foreshortening factors. Depending on orientation, the included angle may appear either larger or smaller than true. Only when the plane is parallel to the view do we see the true angle; when it is perpendicular, the feature may collapse ambiguously.

Step-by-Step Solution:

Verification / Alternative check:
Create an auxiliary view with the plane made parallel to the projection plane; the auxiliary recovers the true angle. Comparing principal and auxiliary views demonstrates the variation in apparent angle.

Why Other Options Are Wrong:

• “Always equals true” holds only when the plane is parallel to the view.
• “Always smaller” or “always larger” ignores orientation dependence.
• Restriction to arcs is irrelevant; angles between straight edges behave similarly.

Common Pitfalls:
Assuming a single foreshortening factor for both angle sides; forgetting to use auxiliary views for true measures; dimensioning an apparent angle instead of the true angle when accuracy is required.

Final Answer:
Correct: the apparent angle may be larger or smaller than true depending on orientation