Question

1. (03.02 lc)

some steps to construct an angle mnt congruent to angle pqr are listed below. step 3 is not listed:
step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.
step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.
step 3:
step 4: join points n and y using a straightedge.
which statement describes step 3 correctly? (5 points)
a. adjust the width of the compass to ab, and draw an arc from point x such that it intersects the arc drawn from n in a point y.
b. adjust the width of the compass to aq, and draw an arc from point x such that it intersects the arc drawn from n in a point y.
c. adjust the width of the compass to bq, and draw an arc from point x such that it intersects the arc drawn from n in a point y.
d. adjust the width of the compass to nx, and draw an arc from point x such that it intersects the arc drawn from n in a point y.

Explanation:

To construct a congruent angle, after creating arcs on the original angle (PQR) and the new angle's side (NT), step 3 requires setting the compass to the distance between the two intersection points (A and B) on the original angle's arcs, then transferring that width to draw an arc from the new angle's arc intersection (X) to find point Y. This ensures the angles have equal measure.

Answer:

Adjust the width of the compass to AB, and draw an arc from point X such that it intersects the arc drawn from N in a point Y.