Using B as center, use the circle tool to draw an circle of any radius that intersects both ray BA and ray BC. Construct points D and E where the circle intersects those rays.

Use the segment tool to construct any radius of the circle you just constructed in Step 2.

Use the Compass tool and select the segment you constructed in Step 3 and then point R to construct a circle centered at R with the same radius as the circle you constructed in Step 2. Construct point S where this circle intersects ray RY.

Construct segment DE.

Use the compass tool and select segment DE and then point S to construct a circle that intersects the circle centered at R that you constructed in Step 4 at point Q.

Draw ray RQ.

Drag point A around and note your observations. Angle QRS should remain congruent to angle ABC.