Question

On her paper, Katarzyna wants to construct the angle bisector of angle LPQR. She has drawn an arc from the vertex point Q that intersects both sides of the angle and has labeled the intersection of the arc with the sides of the angle with P and R. Using a compass and straightedge, what next step must she take to construct the angle bisector?
Option #1: Move the compass further apart and place the pointed end at point Q and draw another arc that intersects the sides of the angle.
Option #2: Place the pointed end of the compass on point P and draw another arc inside the first arc and between two sides of the angle.
Option #3: Place the pointed end of the compass on point P and draw another are outside the first arc an betweon two sides of the angle.
Option #4: Draw a line extending fron the vertex point Q through the middle of the angle.

Answer 1

To construct the angle bisector of angle LPQR after drawing the initial arc from point Q that intersects the sides of the angle at points P and R, the next essential step is to place the pointed end of the compass on point P and draw another arc that intersects the first arc.

The correct option is:

**Option #2: Place the pointed end of the compass on point P and draw another arc inside the first arc and between the two sides of the angle.**

This arc will then be used to intersect with an arc drawn from point R, allowing you to find the point that is equidistant from both sides of the angle. This intersection will then be used to draw the bisector line, completing the construction.