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SAI International School

CLASS – VI

Mathematics

Chapter-14: Practical Geometry - 5
Lesson Notes – 5

SUBTOPICS:

1) ANGLES
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 Some angles of special measures such as 90 , 45 , 60 , 30 ,120 ,135 do not require
the use of the protractor.
 There are some elegant and accurate methods to construct the above angles of
special sizes.
2) CONSTRUCTING AN ANGLE OF A GIVEN MEASURE

a) CONSTRUCTING A 60° ANGLE
Step 1: Draw a line l and mark a point O on it.
Step 2: Place the pointer of the compasses at O and draw an arc of convenient radius
which cuts the line PQ at a point say, A.
Step 3: With the pointer at A (as centre), now draw an arc that passes through O.
Step 4:

b) CONSTRUCTING A 30° ANGLE
Construct an angle of 60° as shown earlier. Now, bisect this angle. Each angle is 30°,
verify by using a protractor.

c) CONSTRUCTING A 120° ANGLE
An angle of 120° is twice of an angle of 60°.
Therefore, it can be constructed as follows :
Step 1: Draw any line PQ and take a point O on it.

Step 2: Place the pointer of the compasses at O and draw an arc of convenient
radius which cuts the line at A.