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Angles in a Box is a puzzle in Professor Layton and the Diabolical Box.

Puzzle

US Version

In the cube below, in the center of three sides of the cube are dots A, B and C. Lines connect the dots.

How many degrees is the angle ABC at the point where lines AB and BC meet? This refers to the internal angle, of course.

UK Version

On the diagram below, A, B and C indicate the centre point of three edges of the cube. These points are connected by lines.

How many degrees is the internal angle ABC at the point where lines AB and BC meet?

Hints




Click a Tab to reveal the Hint.

There's no need to do any complicated calculations. Visualization is the important part.


The three points are each in the center of the sides of a regular cube.

The three points are each in the middle of a side on a regular cube. Think about the other center points. What would happen if you continued connecting center points in this fashion?

Think about the regular geometric figures you can create with points A, B and C.


You could create a regular hexagon, couldn't you? And the internal angles of regular hexagons are always 120 degrees.


Solution

Incorrect

Too bad!

This problem is more about visualization than calculation.

Correct

Good job!

The answer is 120 degrees.

US Version

If you continued to connect the middle points of sides in this way, you would draw a regular hexagon. And the internal angles in regular hexagons are always 120 degrees!

UK Version

If you continued to connect the middle points of the edges in this way, you would draw a regular hexagon. And the internal angles in regular hexagons are always 120 degrees!

DB146S

A big thanks to http://professorlayton2walkthrough.blogspot.com