Lines and Angles
87. Angle Classifiers · Acute, Right, Obtuse, Straight & Reflex
As point B moves around the circle, the measure of ∠AOB changes and its angle type updates accordingly.
Angles are classified by measure: acute (< 90°), right (= 90°), obtuse (90°–180°), straight (= 180°), reflex (180°–360°), complete (= 360°). Drag B around the circle to see the type change as ∠AOB grows.
What this lesson covers
Try to break it
Can you make it exactly 90°? What about 180°? Try to hit each category: acute, right, obtuse, straight, and reflex!
How you build it
Place vertex O and point A and draw ray OA; then place point B and draw ray OB.
- Place vertex O.
- Place point A to the right of O.
- Draw ray OA — the fixed arm of the angle.
- Place point B to set the angle opening — slide it around the circle to see acute, right, obtuse and reflex angles.
- Draw ray OB, then read the angle type named on the canvas.
The proof, step by step
Prove that the type of an angle is decided by its measure.
- An angle measuring less than 90° is called an acute angle.
- An angle measuring exactly 90° is called a right angle.
- An angle measuring more than 90° but less than 180° is called an obtuse angle.
- An angle measuring exactly 180° is called a straight angle.
- An angle measuring more than 180° but less than 360° is called a reflex angle.
Worked example
In a triangle ABC, angle A measures 45°, angle B measures 90°, and angle C measures 45°. Which of the following correctly classifies these three angles respectively?
Angle A (45°) is acute (<90°). Angle B (90°) is right. Angle C (45°) is acute (<90°). Thus, the correct classification is Acute, Right, Acute.
- Acute, Right, Acute — correct
- Right, Obtuse, Acute
- Acute, Acute, Obtuse
- Right, Right, Straight