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In this lesson, let us construct some special angles by without using the protractor.
 
i) Construction of 60° angle:
 
Step 1: First draw a straight line, and mark a point A on it.
 
pic 18.svg
 
Step 2: Take the point A as centre, draw an arc of convenient radius to the line to meet at a point B.
 
pic 19.svg
 
Step 3: With the same radius, take B as centre, draw an arc to cut the previous arc at C.
 
pic 20.svg
 
Step 4: Join AC. Then ∠BAC is the required angle with the measure 60°.
 
pic 21.svg
 
 
ii) Construction of 135° angle:
 
Step 1: First draw a straight line, and mark a point A on it.
 
pic 22.svg
 
Step 2: Take the point A as centre, draw an arc as below which meet at a point B.
 
pic 23.svg
 
Step 3: Take radius, and draw an arc for 60°, as shown above. This cuts an arc at point C.
 
pic 24.svg
 
Step 4: Now take C as centre, draw an arc to with the same radius, point it as D. Here the point D gives the angles of 120°.
 
pic 25.svg
 
Step 5: With the same radius, draw an arc from the point D that cuts the E which gives the 180°.
 
pic 26.svg
 
Step 6: Finally, draw the angle bisector between the two points D (120°) and E (180). The angle bisector separates the two points D and E and gives the angle 150°. Now again find the angle bisector between 150° and 120°, the resultant gives the required angle 135°.
 
pic 27.svg
 
The measure of 135° angle, can be drawn in many ways, without using the protractor. Refer the below video for further information and clarification to construct the 135° angle.
 
Construct 135° degree using ruler and compass: