Alex wants to construct a line segment through R that makes the same angle with line segment QR as line segment PQ. The figure below shows a step to construct a congruent angle at R:

Question

A line segment QR is drawn. PQ is a line segment that makes an obtuse angle of about 120 degrees with QR. An arc, indicating the measure of angle PQR, intersects PQ at S and QR at T. Another arc drawn from point R is a reflection of the first arc but of the same measure and intersects QR. A compass with its ends at points S and T is shown.

Which figure shows the next step to construct a congruent angle at R?

A line segment QR is drawn. PQ is a line segment that makes an obtuse angle of about 120 degrees with QR. An arc, indicating the measure of angle PQR, intersects PQ at S and QR at T. Another arc drawn from point R is a reflection of the first arc but of the same measure and intersects QR. A line segment RX is drawn that makes the same angle with QR as QP makes with QR. A straightedge is placed along the length of RX.
 A line segment QR is drawn. PQ is a line segment that makes an obtuse angle of about 120 degrees with QR. An arc, indicating the measure of angle PQA line segment QR, is drawn. PQ is a line segment that makes an obtuse angle of about 120 degrees with QR. An arc, indicating the measure of angle PQR, intersects PQ at S and QR at T. Another arc drawn from point R is a reflection of the first arc but of the same measure and intersects QR. A straightedge is placed along arc ST.
 A line segment QR is drawn. PQ is a line segment that makes an obtuse angle of about 120 degrees with QR. An arc, indicating the measure of angle PQR, intersects PQ at S and QR at T. Another arc drawn from point R is a reflection of the first arc but of the same measure and intersects QR. A compass is shown drawing a small arc to intersect the big arc near R.
 A line segment QR is drawn. PQ is a line segment that makes an obtuse angle of about 120 degrees with QR. An arc, indicating the measure of angle PQR intersects PQ at S and QR at T. Another arc drawn from point R is a reflection of the first arc but of the same measure and intersects QR. A compass is shown drawing an arc between PQ and QR from point S.

GPT-4o mini · Answer

To construct a line segment through point R that makes the same angle with line segment QR as line segment PQ does, we need to complete the construction after drawing the arcs from point R. Here’s a breakdown of what’s already been done and what comes next:

You have line segment QR and line segment PQ that create an obtuse angle (around 120 degrees).
You’ve marked the intersections of the arcs from PQ and QR with points S and T.
You’ve drawn another arc from point R that’s a reflection of the first arc, intersecting QR.

Now, the next step involves using the compass to ensure that the angle formed by the new segment RX at point R matches the angle formed by PQ and QR.

Among the options, the correct one for the next step would be:

A line segment QR is drawn. PQ is a line segment that makes an obtuse angle of about 120 degrees with QR. An arc, indicating the measure of angle PQR, intersects PQ at S and QR at T. Another arc drawn from point R is a reflection of the first arc but of the same measure and intersects QR. A compass is shown drawing a small arc to intersect the big arc near R.

This option describes the necessary step where you use the compass to create a small arc that helps mark the angle at point R, allowing you to construct line segment RX to ensure that it matches the angle formed by PQ at point P.