Question

arrange the following steps of construction in the right order so as to construct an angle that is congruent to ∠a
answer
place the compass at a. draw an arc that intersects both rays of. label the points of intersection b and c. without changing the setting, place the compass point on x and draw an arc. label the intersection y
∠yxz≅∠bac
draw a ray with endpoint x
place the compass point at c, and open the compass to the distance between b and c. without changing the setting, place the compass point on y and draw an arc. label the point z where the two arcs intersect
use a straightedge to draw \overrightarrow{xz}

Explanation:

Step1: Start with a ray

Draw a ray with endpoint X.

Step2: Copy the arc from angle A

Place the compass at A. Draw an arc that intersects both rays of ∠A. Label the points of intersection B and C. Without changing the setting, place the compass point on X and draw an arc. Label the intersection Y.

Step3: Copy the length BC

Place the compass point at C, and open the compass to the distance between B and C. Without changing the setting, place the compass point on Y and draw an arc. Label the point Z where the two arcs intersect.

Step4: Complete the angle

Use a straightedge to draw $\overrightarrow{XZ}$. And we get ∠YXZ ≅ ∠BAC.

Answer:

1. Draw a ray with endpoint X.
2. Place the compass at A. Draw an arc that intersects both rays of ∠A. Label the points of intersection B and C. Without changing the setting, place the compass point on X and draw an arc. Label the intersection Y.
3. Place the compass point at C, and open the compass to the distance between B and C. Without changing the setting, place the compass point on Y and draw an arc. Label the point Z where the two arcs intersect.
4. Use a straightedge to draw $\overrightarrow{XZ}$.
5. ∠YXZ ≅ ∠BAC