Please help

Question

David constructed angle ABC and needs to double the angle by constructing a copy of the angle using ray BA as one of the sides of the new angle. He has constructed an arc, what next step must he take to construct a copy of the angle using ray BA?

Answer 1

To double angle ABC using ray BA as one of the sides of the new angle, David can follow these steps after constructing the arc:

1. Label the intersections: Let the arc he constructed intersect ray AC at point D and ray AB at point E.

2. Construct the circle: With point E (on ray AB) as the center and the distance ED (from E to D) as the radius, draw an arc that intersects ray BA. This arc will intersect ray BA at some point F.

3. Mark the intersection: Let the point where the new arc intersects ray BA be point F.

4. Construct the new angle: Now, using point B as the vertex, draw a line from B through point F. The angle ABF is now double the original angle ABC.

5. Check the angles: If desired, he can measure and check that angle ABF is indeed double angle ABC.

By following these steps, David will successfully construct a new angle, effectively doubling the original angle ABC.