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To construct an angle of 60 degrees using a compass, follow these steps: Start by drawing a straight line segment (the base) using a ruler. Place the pointed end of the compass on one end of the base and open the compass so that the pencil end touches the other end. Without changing the compass width, place the pointed end of the compass on the same endpoint of the base and draw an arc that intersects the base line. Keep the compass width the same and place the pointed end of the compass on the intersection point of the arc and the base line. Draw another arc that intersects the first arc. Without changing the compass width, place the pointed end of the compass on the endpoint of the base line that was not used previously. Draw an arc that intersects the second arc. Without changing the compass width, place the pointed end of the compass on the intersection point of the second arc and the base line. Draw a straight line segment from this intersection point to the endpoint of the base line. The angle formed by the base line and the last line segment you drew is an angle of 60 degrees. Make sure to use a ruler for the straight lines and keep the compass width consistent throughout the construction.