MYP 1 Mathematics · Geometry

Angle sum properties and construction with protractor

Get started

What Is an Angle?

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°.

Analogy

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:

Three-Letter Angle Notation

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.

Note

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.

Common Mistake

Students sometimes list the three letters in the wrong order. Remember: vertex in the middle, always.

Free preview

11 more sections in this topic

Pick this up in your Library: it holds the whole topic, notes, cheatsheet and questions.