Triangles Contain 180°
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In a triangle, the three interior angles always add to 180°:A + B + C = 180° |
Try it yourself (drag the points):
geometry/images/triangle.js?mode=angles
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)
runs parallel to the base of the triangle.
Notice that:
- angles A are the same
- angles B are the same
And you can see that A + C + B rotates from one side of the straight line to the other, or a full 180°
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