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1)draw a ray OB & OA.
2)with o as a center with any radius, draw an arc which cuts the ray OA & OB at C & D respectively.
3)again take a compass with C & D as a center and with the radius more than half of CD and draw an arc to intersects each other.
4)name the intersecting point as E.
5)through O,E draw a ray which is the recognized angle of a given angle

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You can construct any angle using a protractor which you will find in every mathematical instrument box. some special angles can also be drawn without the use of protractor using only compass and ruler like 60, 90, 45, 15, 75, 120 etc.
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