Angle Bisectors with Randomly Rotated Angles (A) - Free Printable

To construct the bisector of an angle, you need to draw a line that splits the angle exactly in half. Here’s how to do it for each angle using just a compass and straightedge (ruler without measurements):

Step-by-step method for any angle:

1. Place the point of your compass on the vertex (the corner) of the angle.
2. Draw an arc that crosses both sides of the angle. Mark those two intersection points.
3. Without changing the compass width, place the compass point on one of those marked points and draw an arc inside the angle.
4. Do the same from the other marked point — so now you have two arcs crossing each other inside the angle.
5. Use your straightedge to draw a line from the vertex through the point where the two arcs cross. That line is the angle bisector!

You’ll repeat this process for each of the four angles shown.

Since I can’t draw here, imagine doing these steps for each numbered box:

- For Angle 1 (acute V-shape): The bisector will go straight down the middle, splitting it into two equal smaller angles.
- For Angle 2 (obtuse, wide open): The bisector will cut it into two equal parts — still obtuse but half as big.
- For Angle 3 (very narrow acute angle): The bisector will be close to either side, right in the middle.
- For Angle 4 (right or near-right angle): The bisector will split it into two 45° angles if it’s exactly 90°, or whatever half its measure is.

Each bisector starts at the vertex and goes through the interior of the angle, dividing it evenly.

Final Answer:
For each of the four angles, use a compass and straightedge to construct the angle bisector by drawing arcs from the vertex and then from the intersections on the sides, connecting the vertex to where the inner arcs meet. This creates a line that divides each angle into two equal parts.