Use the image to answer the question.

Question

An illustration shows angle X Y Z. Ray Y X and ray Y Z extend from vertex Y indefinitely. Both points X and Z are intersected by a single arc.

Isha constructed ∠XYZ
and needs to double the angle by constructing a copy of the angle using ray YX
as one of the sides of the new angle. He has constructed an arc, as appears in the image. What next step must he take to construct a copy of the angle using ray YX
?

(1 point)

Answer 1

To complete the construction of a double angle using ray YX as one side, Isha should follow these steps:

1. Mark the Intersection Points: Identify the two intersection points where the arc intersects rays YX and YZ. Label these points as points A (intersection with ray YX) and B (intersection with ray YZ).

2. Construct the Arc: Keeping the compass at point A, draw an arc above and below ray YX to mark two points on this arc. Label these points as C and D.

3. Measure the Arc: Without changing the length of the compass, measure the distance between points B and A. Then, adjust the compass to this length.

4. Copy the Arc: Place the compass point at point C (or D), and draw an arc that intersects with the arc created from point A above and below.

5. Connect the Points: Now, connect points C and the new intersection points (E, where the arcs meet). This will create the new ray that forms the new angle ∠XYZ.

6. Final Adjustment: The angle ∠YXE represents the doubled angle, completing the construction.

In summary, after constructing the arc and marking the intersecting points, the next critical step is to set the compass to the distance AB and transfer it to create two arcs from point A.