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

Question

(1 point)

Answer 1

To construct an angle that is both congruent and adjacent to a given angle, you can use a straightedge and a compass in the following steps:

1. Start by drawing a line segment, which will serve as the base for the given angle.

2. Place the compass on one endpoint of the base and draw an arc that intersects the base line.

3. Without changing the compass width, place the compass on the other endpoint of the base and draw another arc that intersects the base line.

4. Using the straightedge, draw a line connecting the intersection points of the two arcs and the base line. This line will be congruent to the given angle.

5. To make the constructed angle adjacent to the given angle, extend the line you just drew beyond the intersection point with the base line.

Now, you have successfully constructed an angle that is both congruent and adjacent to the given angle using a straightedge and a compass.