Question

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what is the next step in constructing an angle (∠mno) congruent to the given angle (∠abc) with a straightedge and a compass?

1. draw a ray. label it no
2. using b as the center and any radius, draw an arc which intersects ba and bc. label the intersection points d and e.
3. ?

draw a ray nm.
using n as the center and any radius, draw an arc which intersects nm and no. label the interception points p and q.
with a straightedge, connect points d and e.
using n as the center and the same radius as before, draw an arc that intersects no. label the arc pq where q intersects no.

Explanation:

Step1: Recall angle - construction steps

The first two steps are drawing a ray for the new angle and creating an arc on the given angle. The next logical step is to create a similar - arc on the new angle setup.

Step2: Analyze options

• Option 1 (Draw a ray NM): This is not the next step as we are still in the arc - drawing phase of the new angle construction.
• Option 2 (Using N as the center and any radius, draw an arc which intersects NM and NO. Label the interception points P and Q): This is incorrect because we need to use the same radius as the arc drawn on the given angle (\(\angle ABC\)).
• Option 3 (With a straightedge, connect points D and E): This is not relevant as connecting D and E does not help in constructing a congruent angle.
• Option 4 (Using N as the center and the same radius as before, draw an arc that intersects NO. Label the arc PQ where Q intersects NO): This is the correct next step as it replicates the arc - drawing step from the given angle to the new angle setup, which is a key part of constructing a congruent angle.

Answer:

Using N as the center and the same radius as before, draw an arc that intersects NO. Label the arc PQ where Q intersects NO.