Fundamental Concepts
16. Angle Classifiers · acute, right, obtuse, straight & reflex
The angle measure updates continuously as B moves along the circular path.
Angles are classified by their measure: acute (< 90°), right (= 90°), obtuse (90°–180°), straight (= 180°), reflex (180°–360°) and complete (= 360°). Drag B around the circle to see the classification change as ∠AOB grows from 0° to 360°.
What this lesson covers
Try to break it
What happens when B crosses the straight line OA? The angle grows past 90° into the obtuse zone, and then hits 180° — a straight angle!
How you build it
Make an angle of any type.
- Place vertex O.
- Place point A to the right of O.
- Draw ray OA.
- Place point B to set the angle opening — try sliding around the circle to see acute, right, obtuse, straight.
- Draw ray OB. Read the angle classifier on the canvas.
The proof, step by step
Your goal: prove that the supplement of an obtuse angle is always an acute angle. Drag the cards into the correct logical order, from the definitions to the conclusion.
- Two angles are supplementary when their measures add up to 180°.
- An obtuse angle measures more than 90° (and less than 180°).
- So the supplement of an obtuse angle equals 180° minus that obtuse measure.
- Subtracting a measure greater than 90° from 180° leaves a result less than 90°.
- An angle less than 90° is acute — therefore the supplement of an obtuse angle is always acute.
Worked example
An angle measures 210°. Which category of angles does it fall into?
Angles between 180° and 360° are called reflex angles. Since 210° falls in this range, it is a reflex angle.
- Acute Angle
- Right Angle
- Obtuse Angle
- Reflex Angle — correct