Explain how you can use a staightedge and a compass to construction an angle that is both congruent and adjacent to a given angle.

First, draw an angle on a sheet of paper. Draw a point at the vertex and label it B. Draw two more points on each ray of the angle. Label those points A and C. Next, using a compass, place the metal point at B. Move the pencil part of the compass at A, then draw an arc through both A and C. (Make sure the compass keeps the same distance between its two arms. This is called the compass's radius.) Then, place the metal point of the compass at A. Draw an arc. Where this arc and the previous arc intersect, place a point. Finally, draw a ray from the vertex, B, through the point you just made.