Angles: 6th grade math lessons for download PDF.

A sixth grade math lesson on angles to develop students’ knowledge and skills in geometry. An angle is a measure of the opening between two straight lines that meet at a common point called the vertex of the angle. It is usually expressed in degrees or radians.
In this chapter, we will study the definition and vocabulary as well as the different types of angles (acute, obtuse, complementary, supplementary, right null, flat, reentrant and salient. Later, we will review the use of the protractor and the bisector of an angle.
A protractor is a tool used to measure angles. It is composed of a flat base or a graduated plate on which is fixed a pivoting rod called mobile arm. It is used by positioning the base on the vertex of the angle to be measured and rotating the movable arm until it is aligned with the two lines forming the angle. The reading of the angle is then done on the scale of the plate. It is used in the fields of geometry, construction, mechanics, topography, etc.
Students will be expected to construct and trace angles and measure with a protractor. The mastery of the different angles and definitions of the course must be mastered since these notions will be recurrent in the sixth grade and throughout your schooling.

I. Notion of angles


An angle is a portion of the plane bounded by two half-lines having the same origin.

1. vocabulary

  • The point O is the vertex of the angle.
  • The half-lines [ox) and [Oy) are the sides of the angle.

definition of an angle

2. scoring

  • The portion of the plane colored in blue is a salient angle.
  • The uncolored portion of the plane is a re-entrant angle.


What is the name of the blue angle?

It can be named in different ways (most often with three letters, the middle one

is always the vertex of the angle): \widehat{xOy},\widehat{yOx},\widehat{BOD},\widehat{DOB},\widehat{BOy},\widehat{yOB},\widehat{DOx},\widehat{xOD}.

3. angles of the same measure


Two angles of the same measure are coded by the same symbol (as for lengths).


In the figure below, what are the angles of the same measure?

These angles are coded with the same symbol, so we have \widehat{EAD}=\widehat{DAC}=\widehat{CAB}.

Angle of the same measure

II. the different types of angles

The angles are classified by category according to their measure.

Different types of angles

III. Use of the protractor


You can measure an angle or draw an angle of a given size with a protractor. The unit is the degree.

Protractor and angle tracing.

Protractor and measuring angles

Did you get that lesson on angles in 6th grade?

Les angles

Un QCM de maths sur les angles en 6ème.

Things to remember:

Skills to assimilate on the angles:

what to remember

  • Know the definition of an acute, obtuse, right and flat angle;
  • Know how to draw an angle using a protractor;
  • To know how to measure with a protractor and to calculate, also, its measure on a geometrical figure;
  • Complementary and supplementary angles;

This course is in accordance with the official programs of thenational education.

In addition, you can continue with the exercises on the bisector of an angle in the sixth grade.

Cette publication est également disponible en : Français (French) العربية (Arabic)

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