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Mia is watching the clock on her wall. You already know the right angle: the square corner, like the corner of a book.
At 1 o'clock, how does the smaller opening between the hands compare to a right angle?
Types of angles
Identify acute and obtuse angles; compare and order angles up to two right angles by size
What a learner can do afterwards
- Classify given angles as acute, right, or obtuse
- Order four angles from smallest to largest by visual comparison
- Identify all acute and obtuse angles in a given triangle or quadrilateral
1 · Read
You already know a right angle: the square corner of a book or a piece of paper. A right angle is a quarter turn. An acute angle has a positive opening smaller than a right angle. An obtuse angle is greater than a right angle and less than a half turn. A half turn is straight, so it is not obtuse. A zero opening is not acute.
Try it together
Use the smaller opening between the hands. At 6 o'clock both openings are half turns, so both are straight. At 1 o'clock it is less than a right angle: acute. At 3 o'clock it is a right angle. At 5 o'clock it is more than a right angle but less than a half turn: obtuse. Smallest to largest: 1, 3, 5, 6.
To classify a shape, inspect each corner one at a time. Compare each corner with the bounds: smaller than a right angle is acute, exactly a right angle is right, and greater than a right angle but less than a half turn is obtuse. Count the corners in each group.
Rotating a whole angle does not change its opening. Lengthening the arms along their own directions does not change the opening either. Two angles of the same type can have different sizes. To order them, compare the actual opening, not the arm length.
An angle with no opening is not acute. Acute means an opening less than a right angle. Obtuse means more than a right angle but less than a half turn. The size of an angle does not change when its arms get longer.
Ten fresh original tasks (x1-x10) authored for this topic, one fresh original reading (original:mt_h0CVtqI2xo:reading3) on the arm-length misconception, three adaptations from actual Khan Academy resources (Angle types review xdd5cdcb6, Types of triangles review x50a6b855, Relate geometric figures to a real-world context x7dfa7f83063bd877), and two Khan Academy videos (Acute, right, & obtuse angles 60129393, Recognizing angles x1781a3d6).
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Where it sits
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Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
Then practise
34 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.