Triangles Contain 180°
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In a triangle, the three angles always add to 180°:A + B + C = 180° |
Try it yourself (drag the points):
We can use that fact to find a missing angle in a triangle:
Example: Find the Missing Angle "C"
| Start With: | A + B + C = 180° | |
| Fill in what we know: | 38° + 85° + C = 180° | |
| Rearrange | C = 180° - 38° - 85° | |
| Calculate: | C = 57° |
Proof
This is a proof that the angles in a triangle equal 180°:
The top
line (that touches the top of the triangle) is
running parallel
to the base of the triangle.
So:
- angles A are the same
- angles B are the same
And you can easily see that A + C + B does a complete rotation from one side of the straight line to the other, or 180°