The angle that leans out
A pencil line goes past a corner by mistake. It makes a new angle with the next side. Is that angle useful?
Step 1 of 4
- A triangle, corners A, B, C.
- Carry side BC on past C.
- The angle it makes with CA is outside the triangle. It is the exterior angle at C.
- It equals the two far corners added: 45° + 55° = 100°.
Carry a side on past the corner
The far corners are A and B, the two not at C. Yes: the new angle equals the far corners added.
Label the corners A, B and C. Carry side BC on past C: make it longer. The new part is a ray from C. This ray and CA make the exterior angle at C. It lies outside the triangle.
The exterior angle and corner C lie on a straight line. So they add to 180°.
A + B + C = 180°, and the exterior angle + C = 180°. So the exterior angle equals the far corners A and B, added.
Check with the figure: C is 80°, so 180 − 80 = 100°. A and B are 45° and 55°, and 45 + 55 = 100°.
Move corner A. Watch the two readings.
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