Angles (With their Types)
ICSE Class 6 · Mathematics · Chapter 24
What this chapter covers
- Angle
- Measuring angles
- Types of angles
- Constructing angles
- Angle bisector
Key definitions
Arms are the two rays that form an angle.
A degree is one of the 360 equal parts of a full turn.
A zero angle is an angle of 0°, in which both arms lie on top of each other.
An acute angle is an angle that measures more than 0° but less than 90°.
A right angle is an angle that measures exactly 90°.
An obtuse angle is an angle that measures more than 90° but less than 180°.
A straight angle is an angle that measures exactly 180°, so that its two arms point in opposite directions and form a straight line.
A reflex angle is an angle that measures more than 180° but less than 360°.
A complete angle is an angle of 360°, made when one arm turns a full circle and comes back to the other arm.
An angle bisector is a ray that starts at the vertex of an angle and divides the angle into two equal angles.
Key points
- An angle is formed by two rays, called arms, that start from one common point, the vertex.
- The vertex letter goes in the middle when an angle is named with three letters, as in ∠ AOB.
- Every angle has an interior between its arms and an exterior outside them.
- Angles are measured in degrees; a full turn is 360°.
- A protractor measures angles; place its centre on the vertex and read the scale that starts at 0° on one arm.
- The length of the arms does not change the size of an angle.
- Types of angles: zero (0°), acute (less than 90°), right (90°), obtuse (between 90° and 180°), straight (180°), reflex (between 180° and 360°) and complete (360°).
- Compasses give 60° with one step of the radius along an arc and 120° with two steps.
- An angle bisector divides an angle into two equal angles.
- Bisecting 60° gives 30°, bisecting 180° gives 90°, and bisecting 90° gives 45°.