Angles (III): Acute, right, obtuse

1Summary 重點摘要

Acute < 90°; right = 90°; obtuse > 90°.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: Three kinds, one boundaryThe three kinds of angle use 90° as the boundary: below 90° is acute, exactly 90° is right, and between 90° and 180° is obtuse. Test with a few values: 45° is acute, 90° itself is right, and 120° is obtuse. Remember the chant: acute is sharp, right is square, obtuse is wide. There is only one rule — compare each angle with 90°: less, equal or greater, and the type follows at once.
2. Part 2: What acute looks likeAcute angles look sharp and narrow, opening less than a right angle. Clocks give ready examples: at 2 o'clock the hands open 60°, an acute angle; at 1 o'clock only 30°, even sharper. Cut a pizza into 8 equal slices and each slice's angle at the centre is 360° ÷ 8 = 45°, under 90°, so every slice is acute. Any angle narrower than a book corner is probably acute, but measuring or a set square confirms it.
3. Part 3: What right angles look likeA right angle is exactly 90°, the only fixed one among the three kinds. Right angles are everywhere: the largest corner of a set square, the four corners of a textbook, window frames, and the corner where a wall meets the floor. A right angle looks square and neat, opening exactly a quarter of a full turn. Compare with the set square's corner: a perfect fit means right — 89° is still acute and 91° is already obtuse.
4. Part 4: What obtuse looks likeObtuse angles are wider than a right angle — more than a quarter turn but less than a half turn. At 5 o'clock the clock hands open 150°, over 90°, a typical obtuse angle; compare it with the 90° right angle at 3 o'clock and the difference is obvious. Daily-life obtuse angles include a door opened past half-way, an opened folding fan, and the angle a leaning ladder makes with the ground. They look very wide, yet official classification still relies on the degrees.
5. Part 5: Sort angles with a set squareA set square is the handiest sorting tool — no measuring needed. Place its right-angle corner over the angle to check: if the angle is narrower than the tool, it is acute; if it fits exactly, it is right; if it is wider, it is obtuse. The principle is using 90° as the standard, since the tool's corner is a physical model of it. This trick is especially useful in tests where protractors are not allowed.
6. Part 6: Practise by degreesClassifying by degrees takes practice, and the key is always comparison with 90°. 30° is acute; 90° itself is right; 91° has just crossed over, so it is obtuse; 179° is close to 180° but has not reached it, so it is obtuse, not a straight angle. Watch two traps: 89° misses a right angle by just 1° yet is still acute, and 100° looks modest but is already obtuse. Classification depends only on the degrees, never on how long the sides are drawn.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Acute < 90°, right = 90°, obtuse > 90°
• Use a set square's right angle as the sorting tool
• Book and window corners are right angles
• Clock: 2 o'clock acute, 3 right, 5 obtuse
• Classify by comparing with 90°, ignoring side length