Let’s first start with construction of simple angular measurements such as 60-degree angles and 90-degree angles before moving on to bisection and finally understanding how to construct a 75 degree angle with a compass.
To start with, first draw a line segment using the straight edge of the protractor using a pencil. Now open the compass and place a Point on one end of the Line Segment drawn. Draw an arc cutting the Line Segment and also above it to create a quadrant of a Circle. Try not repositioning and adjusting the compass. Next arc to be drawn should intersect the first arc. Connect the Intersection point of arcs with starting point on the line segment, using the straight edge of protractor. Measure 60-degree angle with your protractor.
To draw perpendicular open the compass such that when point is placed on one end of the segment, the pencil touches the other end. Draw two small arcs using the compass at the estimated center of line segment, above and underneath. Repeat the same procedure keeping the point of the compass on other end of line segment. After you get two cuts above and underneath the line, draw a line segment passing through these intersection points of arc. The angle we get is 90° to the line segment.
To draw bisector of 60 degree place compass on the point where 60 degree is subtended and stretch it to the point of intersection of two arcs from where 60 degree line segment is passing. With this measure draw an arc on the original line segment. Next cut two arcs by placing compass on this arc intersection with line and intersection point of arcs at 60° to get an intersection point for 30 degree angle.
Follow the same approach to get 15 degree. The required 75 degree can be found by subtraction 15 degree from the previously drawn 90 degree.