If an angle can be divided in half by constructing a bisector, then what method doubles an angle?

Answer 1

To double an angle, you can use a geometric construction method known as the "angle doubling" construction. Here's a simple way to do it:

1. Start with the angle: Let’s say you have angle \( \angle AOB \).

2. Construct the angle: Draw rays \( OA \) and \( OB \) to show the angle.

3. Draw an arc: With the center at point \( O \) and a suitable radius, draw an arc that intersects both \( OA \) and \( OB \). Label the intersection points as \( P \) and \( Q \).

4. Construct extended lines: From points \( P \) and \( Q \), draw arcs of the same radius that intersect each other. This creates points where these arcs intersect; label the intersection as \( R \).

5. Draw the final ray: Draw a line from point \( O \) through point \( R \). The angle \( \angle AOB' \) will now be twice the measure of the original angle \( \angle AOB \).

This construction effectively creates an angle that is double the original angle \( \angle AOB \).