Two angles and the side between
You draw a base. At each end you draw a ray at an angle. Do the two rays meet?
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Step 1 of 4
- A base, and a ray at 55° from the left end.
- A ray at 80° from the right end. They meet.
- At 125°, the rays run side by side.
- At 140°, the rays spread apart.
The rule
Sometimes: they meet when the two angles add to less than 180°.
Take two angles at the ends of a side. A triangle exists when their sum is less than 180°. If the sum is 180° or more, it does not. The side length does not matter. The third angle is 180° minus their sum.
| Angles | Sum | Triangle? | Third angle |
|---|---|---|---|
| 38° and 64° | 102° | Yes | 78° |
| 120° and 59° | 179° | Yes | 1° |
| 90° and 90° | 180° | No | none |
| 100° and 85° | 185° | No | none |
At 179° the triangle is very thin. It still exists.
If the angles add to 180°, the rays run side by side. They never meet. Over 180° they spread apart.