(geometry) explain how you can use a straightedge and a compass to construct an angle that is both congruent and adjacent to a given angle.

Use the straightedge to draw two parallel lines and then you draw a line that goes through them that is perpendicular. You then use the compass to measure the angles, they should be congruent and adjacent.

Mark an arc through the sides of the angle. Let the arc intersect the rays at A and B. Continue the arc on past B for a distance. 

Set the compass at B, and to the width of AB. 

Still with the compass at B, mark an arc to intersect the first arc at C. 

Now you have AB = BC. 

Since the radius OA=OB=OC, angles AOB and BOC are congruent.

Just turn the whole gym into pie