in two to three sentences, explain how you can use a straightedge and a compass to construct an angle that is both congruent and adjacent to a given angle.
To construct an angle that is congruent and adjacent to a given angle using a straightedge and a compass, you would first use the compass to draw an arc that intersects both sides of the given angle. Then, using the straightedge, draw a line segment connecting the intersection points of the arc and the given angle. This line segment will be the side of the newly constructed angle that is adjacent and congruent to the given angle.
To construct a congruent and adjacent angle to a given angle using a straightedge and compass, follow these steps:
1. Place the compass at the vertex of the given angle, and draw an arc that intersects both sides of the angle.
2. Without changing the compass width, place the compass's point on one of the intersection points, and draw an arc that cuts through the given angle.
3. Use a straightedge to draw a line connecting the vertex of the given angle to the intersection point on the opposite side. The constructed angle will be congruent and adjacent to the given angle.