How can I estimate whether an angle is acute, right, or obtuse?

Use a square corner of paper as your reference. Match that corner to the indicated opening of the angle in the diagram, lining up the paper corner’s point with the angle’s vertex. Compare the openings, not the lengths of the lines.

If the indicated opening is narrower than the paper corner, estimate it as acute. If it matches, estimate it as right. If it opens wider, estimate it as obtuse, as long as the indicated angle is less than 180°. The definitions are: acute is less than 90°, right is 90°, and obtuse is between 90° and 180°. [S1]

For example, if the indicated opening looks slightly wider than the paper corner, your estimate is obtuse. Treat that as a first check, especially if the drawing is rough.

The angle can be tilted; it does not need to point up or sit on a horizontal line. Match the paper corner’s point to the angle’s vertex, then turn the paper so one edge of the corner follows one ray. A ray is one of the two arms that starts at the vertex. Compare the indicated space between the two rays with the space between the paper corner’s edges.

Keep the vertex lined up while you compare. Don’t compare the paper corner to the outside of the indicated angle or to a line’s length. If the paper is too large or blocks the diagram, you can trace just its corner onto a scrap and use that small reference.

Not by appearance alone. A diagram may be approximate, and a small difference can be hard to see. If you need a dependable classification, measure the angle with a protractor rather than deciding from how the drawing looks. Put the protractor’s center at the vertex and align its baseline with one ray, then read where the other ray crosses the scale. [S1]

For instance, suppose a sketch seems a little wider than your paper corner but the edges are faint. Record “possibly obtuse” as your estimate, then measure if the answer matters. The estimate does not tell you an exact degree measure, and the picture alone does not establish whether it was drawn precisely.

Try this routine:

1. Find the vertex, the two rays, and the opening the diagram indicates.
2. Line up a square paper corner at the vertex and along one ray.
3. Compare the openings: narrower than the corner means estimate acute; about equal means estimate right; wider means estimate obtuse, provided the indicated angle is less than 180°.
4. If it is close or the sketch is unclear, use a protractor if one is available. Align its center with the vertex and its baseline with one ray. [S1]
5. If you cannot measure, label your result as an estimate rather than claiming an exact angle.

A note you can copy is: “Compared with a right-angle paper corner, this indicated opening looks [narrower/about equal/wider], so I estimate it is [acute/right/obtuse]. I would measure it if an exact check is needed.” The comparison helps classify a drawing, but it does not verify how accurately the diagram represents a measured angle.