Hand-drawn geometric diagram showing angle construction with points A, C, D, E and an angle labeled 75 degrees.

Draw a Base Line: Use your straightedge to draw a horizontal line. Let's call one endpoint of this line 'A'. This will be one ray of our 75-degree angle. We want the vertex of the angle to be at point 'A'. Construct a 60-degree Angle: Place the point of your compass on point 'A'. Open your compass to any convenient radius (width). Draw an arc that intersects the horizontal line at a point we'll call 'B'. Without changing the radius of your compass, place the point of the compass on point 'B'. Draw another arc that intersects the first arc. Let's call this intersection point 'C'. Use your straightedge to draw a line from point 'A' through point 'C'. The angle ∠BAC is now a 60-degree angle. Bisect the 60-degree Angle to Create a 30-degree Angle: Place the point of your compass on point 'B'. Open your compass to a radius greater than half the distance between 'B' and 'C'. Draw an arc in the interior of the 60-degree angle. Without changing the radius, place the point of your compass on point 'C'. Draw another arc that intersects the first arc drawn in this step. Let's call this intersection point 'D'. Use your straightedge to draw a line from point 'A' through point 'D'. The angle ∠BAD is now a 30-degree angle (since it bisects the 60-degree angle ∠BAC). Construct a 90-degree Angle (Perpendicular Line) at Point A: Place the point of your compass on point 'A' and draw an arc intersecting the base line at two points, let's call them 'E' and 'F' (make sure 'A' is the midpoint of See more