Explain how you can use a straightedge and a compass to construct an angle that is both congruent and adjacent to a given angle.
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To construct an angle that is both congruent and adjacent to a given angle, follow these steps:
1. Begin by drawing the given angle. Label its vertex as point A.
2. Place the compass point on point A and draw an arc that intersects both sides of the given angle. Label these points of intersection as B and C.
3. Without changing the compass width, place the compass point on point B and draw an arc that intersects the ray of the given angle. Label this point of intersection as D.
4. Without changing the compass width, place the compass point on point C and draw an arc that intersects the ray of the given angle. Label this point of intersection as E.
5. With the compass width still intact, place the compass point on point D and draw an arc that intersects the arc drawn from point C. Label this point of intersection as F.
6. Using a straightedge, draw a line segment from point A to point F.
Now, the angle with vertex A formed by the sides AF and AB is congruent and adjacent to the given angle.