Explain how you can use a straightedge and a compass to construct an angle that is both congruent and adjacent to a given angle.
There are many simple youtube videos that show the above method described by Steve, here is one of them
https://www.youtube.com/watch?v=K7TAXoSYui4
Y'all should actually watch that videoooo
I was stuck on this question for like 2 weeks and i didn't wanna write down something that would make me look silly. HAAH
BUT I FINALLY GOT THE ANSWER literally just write down everything that lady says, its super easy
GOOD LUCK
Draw two intersecting lines, using the straightedge. The lines form an angle. Label the vertex of the angle as point O.
Set the compass to a convenient radius and using point O as the center, draw a circle. The circle will cut the sides of the angle. Label the two points of intersection A and B.
Set the compass at A and draw a circle so that it contains point B. That circle will intersect the first circle. Label the point of intersection as C.
Since arc AB is the same length as arc AC, the two arcs subtend congruent angles. Since the two angles share side OA, they are adjacent.
I feel like nobody takes into account that it says, "given angle"
To construct an angle that is congruent and adjacent to a given angle using a straightedge and a compass, follow these steps:
1. Begin with the given angle, let's call it angle A.
2. Place your compass at one of the vertex points of angle A and draw an arc that intersects both sides of the angle. Label the points of intersection as B and C.
3. Without changing the compass width, place the compass at point B. Draw another arc that intersects the first arc you drew. Label the point of intersection between the arcs as D.
4. Using the straightedge, draw a line connecting point B and point D. This line will be congruent to one of the sides of angle A. Label the point of intersection between this line and the other side of angle A as E.
5. Using your compass, place the compass at point E and adjust its width to the distance between points E and B. Without changing the compass width, draw an arc from point D.
6. Using your straightedge, draw a line connecting point D and the point of intersection between the second arc and the line you drew in step 4. This line will be congruent and adjacent to angle A.
To summarize, you are essentially constructing a copy of one side of the given angle and then using that side to create an adjacent congruent angle.