Lines and Angles
85. The Birth of an Angle · two rays, one vertex, infinite possibilities
The opening between the two rays always defines a single angle measure.
An angle is formed by two rays sharing a common endpoint (the vertex). The "opening" between the rays is measured in degrees (°). Angles range from 0° (rays coincide) to 360° (full rotation).
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For subscribers · Selina ICSE: Lines and Angles
What this lesson covers
Try to break it
Try to break it — drag B any way you like. The opening always defines an angle, even when it’s a straight line! Watch the measurement update.
How you build it
Place the vertex O, then draw two rays from it to form an angle.
- Click anywhere to place the vertex O.
- Draw a horizontal ray starting from O.
- Draw the second ray from O to complete the angle.
The proof, step by step
Prove that two rays from a common vertex form one angle.
- An angle consists of a vertex and two arms (rays).
- The size of an angle depends on the amount of rotation between the arms, not their length.
- Angles are measured in degrees (°), where one full turn equals 360°.
Worked example
In the given figure, two rays OA and OB originate from a common point O. If the opening between them measures 45°, what is the measure of ∠AOB?
By definition, the measure of an angle formed by two rays sharing a common endpoint is exactly the amount of opening between them. Since the opening is given as 45°, ∠AOB = 45°.
- 45° — correct
- 135°
- 90°
- 180°