How can you use a straightedge and a compass to construct an angle that is both congruent and adjacent to given angle?

Answer 1

To construct an angle that is both congruent and adjacent to a given angle using a straightedge and compass, first, draw a ray from the vertex of the given angle. Then, place the compass point at the vertex of the given angle and draw an arc that intersects both rays of the angle. Without changing the compass width, place the compass point at the intersection of the arc and one ray, and draw an arc. Finally, repeat this step from the vertex of the new ray to create a congruent angle, and connect the vertex to the intersection of the arcs to form the desired angle.