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Year 7 Interactive Maths - Second Edition


Angles

Angles are used in daily life.  Engineers and architects use angles for designs, roads, buildings and sporting facilities.  Athletes use angles to enhance their performance.  Carpenters use angles to make chairs, tables and sofas.  Artists use their knowledge of angles to sketch portraits and paintings.


If two lines meet (or intersect) at a point, then an angle is formed.  The point of intersection of the lines is called the vertex.

An angle is shown below.

An angle

Lines AB and AC meet at the point A to form an angle.  The point A is the vertex of the angle, and the lines that meet to make the angle are called the arms of the angle.


Naming Angles

An angle is named by using the names of the points on the arms, with the name of the vertex in the middle.


Size of an Angle

The amount of turn from one arm of the angle to the other is said to be the size of an angle.

The angle size measures the amount of turn from one arm to the other


The size of an angle is measured in degrees; and the symbol used to represent degree is .  There are 360 in a full turn (or circle).

A full turn has 360 degrees

 



Note:

A degree is defined such that the angle of one full turn (or circle) is 360 degrees.


Measuring Angles

A protractor is used to measure angles.  In this section, we will consider the use of a protractor that has the shape of a semi-circle and two scales marked from 0 to 180.

A protractor


The two scales make it easy for us to measure angles facing different ways.
These angles can be measured by a protractor


To measure the size of angle ABC, place the protractor over the angle so that the centre of the protractor is directly over the angle's vertex, B; and the base line of the protractor is along the arm, BA, of the angle.

Using a protractor to measure angle ABC

We use the inner scale to measure the angle ABC, as the arm AB passes through the zero of the inner scale.  Following the inner scale around the protractor, we find that the other arm, BC, passes through the inner scale at 60.  So, the size of angle ABC is 60 degrees. We write this as follows:

angle ABC = 60 degrees


To measure the size of angle PQR, place the protractor over the angle so that the centre of the protractor is directly over the angle's vertex, Q; and the base line of the protractor is along the arm, PQ, of the angle.

Using a protractor to measure angle PQR

We use the outer scale to measure the angle PQR, as the arm PQ passes through the zero of the outer scale.  Following the outer scale around the protractor, we find that the other arm, QR, passes through the outer scale at 120.  So, the size of angle PQR is 120 degrees.  We write this as follows:

angle PQR = 120 degrees


Types of Angles

Angles are classified according to their size.


An acute angle is greater than 0 and less than 90.

An acute angle


A right angle equals exactly 90.

A right angle

Note that a right angle is marked on the diagram as a small square.


An obtuse angle is greater than 90 and less than 180.

An obtuse angle


A straight angle equals exactly 180.

A straight angle


A reflex angle is greater than 180 and less than 360.

A reflex angle


A perigon (or a revolution) is an angle that equals exactly 360.

A perigon (or revolution)


Measuring Reflex Angles

Recall that:

A protractor can be used to measure the size of an acute angle (between 0 and 90) and an obtuse angle (between 90 and 180).


Now, we will use a protractor to measure the reflex angle PQR.

The reflex angle PQR

To measure the reflex angle PQR, extend the arm PQ to A to form angle PQA which is a straight angle.  Then measure the size of the angle AQR and add 180.

Using a protractor to measure the reflex angle PQR

Reflex angle PQR = 235 degrees


Key Terms

point, angle, vertex, arms of the angle, size of an angle, degrees, protractor, inner scale, outer scale, acute angle, right angle, obtuse angle, straight angle, reflex angle, perigon, revolution


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