Angles
Constructing an angle of a given measure
Suppose we want an angle of measure 40°.
Here are the steps to follow :

Step 1     Draw AB of any length.

Step 2     Place the centre of the protractor at A and the zero edge along AB.

Step 3     Start with zero near B. Mark point C at 40°.

Step 4     Join AC. BAC is the required angle.

Bisector of an angle
Construction with ruler and compasses
Let an angle, say, A be given.

Step 1     With A as centre and using compasses, draw an arc that cuts both rays of A . Label the points of intersection as B and C.

Step 2    With B as centre, draw (in the interior of A ) an arc whose radius is more than half the length BC.

Step 3    With the same radius and with C as centre, draw another arc in the interior of A. Let the two arcs intersect at D. Then AD  is the required bisector ofA .

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