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construct an angle of 60 degree and bisect it.

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Follow the following steps of construction to draw an angle measuring 60°and further bisect it.1. Draw a straight line AB and take any point P on it.2. With P as center and with small radius, draw an arc intersecting the line AB at two points C and D3. With the same radius and taking C as center, draw another arc intersecting the first arc at  E.4. Join PE and extend it to point F. Then ∠FPA=60°Bisect ∠FPA. 5. With C as center and with small radius, draw an arc in between the  ∠FPA6. With the same radius and taking E as center, draw another arc intersecting the previousarc at G.7. Join PG Then ∠GPA=30°



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We know that the angles in an equilateral triangle are all 60º in size.  This suggests that to construct a 60º angle we need to construct an equilateral triangle as described below.

Step 1:  Draw the arm PQ.
Step 2:  Place the point of the compass at P and draw an arc that passes through Q.
Step 3:  Place the point of the compass at Q and draw an arc that passes through P.  Let this arc cut the arc drawn in Step 2 at R.


 

 

So, to bisect a 60º angle and then bisect it. Often, we apply the following steps.

Step 1:  Draw the arm PQ.
Step 2:  Place the point of the compass at P and draw an arc that passes through Q.
Step 3:  Place the point of the compass at Q and draw an arc that cuts the arc drawn in Step 2 at R.
Step 4:  With the point of the compass still at Q, draw an arc near T as shown.
Step 5:  With the point of the compass at R, draw an arc to cut the arc drawn in Step 4 at T.
 

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