What Is an Angle?
An angle is the amount of turn between two straight lines (called arms) that meet at a common point called the vertex.
Think of an angle as a measure of rotation — how far you would need to spin one arm to reach the other. Angles are measured in degrees (°), and a full turn all the way around is 360°.
Imagine the hands of a clock. At 3 o'clock, the minute hand and hour hand form a 90° angle. At 6 o'clock, they form a straight line — 180°. A full revolution of the minute hand takes it back to the start: 360°.
Every angle has three important parts:
- Two arms — the straight lines that form the angle
- A vertex — the point where the two arms meet
- The arc — the curved symbol drawn between the arms to show which angle is being measured
Naming Angles Correctly
When a diagram has more than one angle at the same point, we need a clear system to say exactly which angle we mean. We use three letters to name an angle precisely:
An angle is named using three capital letters: the first letter is a point on one arm, the middle letter is always the vertex, and the third letter is a point on the other arm. The symbol ∠ is written before the letters.
For example, ∠DAC means the angle measured at vertex A, with one arm going towards D and the other towards C.
The vertex letter must go in the middle. Compare ∠DAC (vertex at A) with ∠DCA (vertex at C) — these use the same three points but describe completely different angles because the vertex has changed. Always double-check which letter is the vertex.
Students sometimes list the three letters in the wrong order. Remember: vertex in the middle, always.
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