Construction of Angles using compass ruler

Angle is a stature formed by two rays. The two rays have a common endpoint which is called the vertex of the angle.

  1. Construction of an angle with a given measure

Draw an angle of 60^\circ using a protector.

Step 1: Draw a line BA.

Step 2: Put the protector on the line in such a way that the centre of the protector lays on point B and the zero edge comes on the line segment BA.

Step 3: Start from 0^\circ and mark the point C at 60^\circ .

Step 4: Join BC.

mathjax]\angle CBA is the required angle.

  1. The bisector of an angle

An angle bisector is the line segment which divides a particular angle into two equal parts. It is also called the line of symmetry of the angle.

Construction of angle bisector (using a ruler and compass)

Draw the angle bisector of \angle O.

Step 1: Put the point on O and draw an arc of any radius so that it cut the rays at point A and B.

Step 2: Put the pointer on point A and draw an arc of the radius of more than half of AB.

Step 3: While taking B as the centre. We will draw an arc of the same radius so that it cut the previous arc at point C.

Step 4: Join OC. OC is the required angle bisector of \angle O.

Hence, \angle BOC = \angle COA.

  1. Angles of special measures

There are some angles which we can construct accurately with the help of a compass without using a protector.

Construction of 60^\circ angle.

Step 1: Draw a line m and mark a point C on it.

Step 2: Take C as the centre and draw an arc of any radius to cut the line at point D.

Step 3: While taking D as the centre we need to draw an arc of the same radius to cut the previous arc.

Step 4: Join CE. \angle C = 60^\circ .

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