Question

Step 3: take the acute triangle and tear off each of the angles from the triangle. arrange the three angles so that their vertices meet at a point. what do you notice?

Answer 1

If we take an acute triangle and tear off each of the angles from the triangle, we are left with three angles that share a common vertex.

We can arrange these angles around the vertex in any order, but they will always sum up to 360 degrees.

This is because the sum of the angles in any triangle is always 180 degrees, so when we tear off all three angles, we are left with no angles in the original triangle. The only way to arrange the three angles around the common vertex is to place them end-to-end in a circle, forming a full circle of 360 degrees.

This is a consequence of the fact that the sum of the angles in any polygon with n sides is always (n-2) * 180 degrees, and in this case we have a polygon with three sides (the torn-off angles) and n-2 = 1, so the sum is 1 * 180 = 180 degrees. Adding this to the 180 degrees of the original triangle gives a total sum of 360 degrees.

Explanation: