TOPIC: ANGLES

CONTENT

DEFINITION OF ANGLES 

TYPES OF ANGLES

BISECTION AND CONSTRUCTION OF ANGLES. 

ANGLES

An angle is formed when two straight lines intersect or meet at a point. 

The sum of angles at the centre of a complete circle is 3600. 

 TYPES OF ANGLES 

1.          Acute angles: – These are angles that are less than 900.

2.          Right angle: – This is an angle that is equal to 900.

3.          Obtuse angles: – These are angles that are greater than 900 but less than 1800.

4.          Reflex angles: – These are angles that are greater than 1800 but less than 3600.

5.          Complementary angles: – These are angles that sum up to 900.

6.          Supplementary angles: – These are angles that sum up to 1800.

EVALUATION

1.          Define an angle.

2.          Mention five types of angles and describe them.

CONSTRUCTION OF ANGLES

The following are several ways of constructing or drawing angles: 

•             Using a setsquare

•             Using a combination of set squares

•             Using a protractor 

•             Using a pair of compasses 

 HOW TO CONSTRUCT ANGLES USING SETSQUARE

Standard angles are angles 300,450, 600, and 900. These angles can be drawn by simply using a set square. The method is simply choosing the appropriate set square that has the angle that is to be drawn. Thus 300-600 setsquare is used to draw 300, 600, and 900. Similarly, the 45-45 set square is used to draw 450 and 900.

 EVALUATION

With the aid of a set square construct the following angle: i)900 ii) 600 iii)450

 COMBINATION OF SET SQUARES 

Set squares can be combined to construct the following angles:

1.          To construct 750, combine 450 and 600 set squares

          1800– (600 +  450)= 750

2.          To construct 1350, combine 450 and 900

         450+ 900 = 1350  

3.          To construct 1050, combine 600 and 450

         450+ 600 = 1350 

 EVALUATION

1.        Combine the sets-square to construct angles 750 and 1350.

2.         Construct angle 600

 HOW TO DRAW AN ANGLE USING A PROTRACTOR

Procedure

1.   Place the protractor on the line from which the angle is to be formed. The baseline marked O at one end and, 180 marked at the other end.

2.    Set the centre of the protractor to start from where the vertex of the angle will be.

3.    Mark the required degree of the angles to be drawn.

4.    Use a straight line to join the marked point at the angle to the point vertex of the angle

 EVALUATION

1.          Measure the following angles using your protractor

1.          a) 880     b)1700       c)2750             d) 3000        e)150

1.          Construct angle 30o

 How to construct Angles Using a Pair of Compasses   

600 

Procedure 

1.          Draw a straight line and mark the centre O.

2.   From O, using a convenient radius at point A, draw an arc (almost a quadrant).

3.          With the same radius draw another arc to intersect the first arc at C.

4.          Draw a line from O through the point of intersection.

The angle formed is 600

900

Procedure 

1.          Draw a straight line and mark the centre O.

2.          From O draw a semicircle to touch the straight line at A and B.

3.          From A, with a longer radius, draw an arc at the centre up.

4.          From B, with a longer radius, draw an arc at the centre up to intersect at C.

5.          Draw a line from O through C.

The angle COA and COB is 900

 BISECTION OF ANGLES

To bisect a given angle

1.          Draw a given angle ABC.

2.          With centre B and any convenient radius draw an arc to cut AB to D and BC at E.

3.          With centre A1 and any small radius of an arc.

4.          With centre E and the same radius draw an arc to intersect the previous one at F.

5.          Join BD, BD bisects angle ABC, i.e. angle ABD= DBC.

6.          Use a protractor to check angles ABF and CBF.

The following angles can be constructed by bisection:

•             300 can be constructed by bisecting 600

•             150 can be constructed by bisecting 300

•             12.50 can be constructed by bisecting 150

•             450 can be constructed by bisecting 900

•             22.50 can be constructed by bisecting 450