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In addition to a compass, you WILL need a straight edge.

Draw a long straight line.

Using the compass and straight edge, and standard procedures, draw a perpendicular bisector of the line.

Then, using other standard geometrical construction procedures, bisect one of the right angles to produce a 45 degree angle.

The remaining right angle and the 45 degree angle next to it will be 135 degrees - as required.

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Q: How do you construct an angle of 135 degrees using compass?
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