Question

how to draw 60 degree angle without using protector

Answer 1

You can draw it using compass and pencil
Make a line
And draw a semi circle from the end point of line
A part of semicircle which is in the line place the compass on it
And draw an arc
Join the lines angle will be of 60 degree
Note. don't disturb the compass while this process

Answer 2

To construct (draw) a 60 degree angle with compass and straightedge or ruler. This construction works by creating an equilateral triangle. Recall that an equilateral triangle has all three interior angles 60°. We use one of those angles to get the desired 60 degree result. See the proof below for more details.

▪Printable step-by-step instructions
The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.

▪ Proof
This construction works by creating an equilateral triangle. Recall that an equilateral triangle has all three interior angles 60°. The image below is the final drawing above with the red items added.

▪ Argument Reason
1) Line segments AB, PB, PA are congruent - All drawn with the same compass width.
2 ) Triangle APB is an equilateral triangle - Equilateral triangles are those with all three sides the same length.
3) Angle APB has a measure of 60° - All three interior angles of an equilateral triangle have a measure of 60°. See Equilateral triangle definition.

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