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Draw a line at the vertex B, parallel to the base AC. With AB as one transversal, and BC another transversal , it can be proved that the three angles of a triangle add up to a straight angle that is 180 degrees.

The angles of a triangle always sum to 180 degrees


the internal angles in a triangle always add up to 180

Internal angle is an angle formed between any two vertices of a triangle. 

The internal angles are located inside the triangles.

Sum of all internal angles of a triangle are equal to 180 degrees

I have uploaded a word document showing why the internal angles of a triangle add up to 180 deg. For a more complete explanation see the following website. http://www.mathsrev...se/pages.php?page=17

If you do not have scissors but you have a pencil: draw a triangle, any triangle. Lie the pencil along one of the sides of the triangle. Rotate the pencil through each of the internal angles and you should find that it is now on the same side where you started, but pointing in the opposite direction. Your pencil has gone through half a turn or 180 degrees.

Another way to convince yourself that the angles add up to 180 degrees: you need a piece of paper and some scissors. Draw a triangle, any triangle (OK so you need a pencil and ruler too). Mark each internal angle. Cut out the triangle. Cut again so that the angles can be put together around a point and you should see that they make half a rotation or 180 degrees. I think that it is easier to do than to describe!

Does that help?

Hey, so the sum of all three angles in a triangle is 180 (in degrees). So when 2 lines meet there is an angle between them, this is going to be a number between 0 and 360. 1000s of years ago when they decided how many degrees should be around a point they thought 360 would be a good number. Now an important rule with shapes is that the sum of the angles inside is always the same, so long as you keep the number of side the shape has the same, it doesn't matter how you stretch it or pull it. So imagine a straight line, which we will call a triangle (you have to use your imagination because a straight line isn't a triangle). But to do this the 2 ends of the line will be 2 of the corners of the triangle. And they will both be 0(degrees) because there is no space between a line and itself. So we have 0+0 as 2 of them, but for it to be a triangle there must be a third corner, which isn't really a corner at all, but again use your imagination. This corner will be somewhere between the to ends, and it will be flat, no bend in it at all. Now we know that around a point there is 360 degrees, so around half a point, or on this straight line, there must be 360/2. Or 180. So 0+0+180=180, which will stay the same even if you stretch the triangle out so it is no longer a flat line

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