Two angles that can be trisected with a straightedge and compass are _____ and _____ angles.

The two angles that can be trisected with a straightedge and compass are 90-degree and 180-degree angles.

Here's how you can do it:

1. For a 90-degree angle:

   • Draw a straight line on the paper.
   • Using the compass, draw an arc intersecting the line.
   • Without changing the compass width, draw another arc intersecting the first one.
   • Draw a line from the intersection point of the arcs to the intersection point with the line. This line divides the 90-degree angle into two 45-degree angles.
   • Repeat the process with one of the 45-degree angles to get three 30-degree angles.

2. For a 180-degree angle (a straight line):

   • Draw a straight line on the paper.
   • Choose a point on the line and draw a circle centered on that point.
   • The circle intersects the line at two points. Draw two more circles, each centered on one of these points, with the same radius as the first circle.
   • The two new circles intersect each other and the first circle. Draw a line from the center point to each of the two intersection points. This line divides the 180-degree angle into three 60-degree angles.