Determining if a triangle is possible given two angle measures
About this video
The video asks how many unique triangles can be drawn with a 110-degree angle and a 75-degree angle. Because the interior angles of any triangle add up to 180 degrees, and these two already add up to 185 degrees, no such triangle can exist.
You'll be able to
- use the fact that a triangle's interior angles add up to 180 degrees.
- decide whether a triangle is possible from two of its angle measures.
Key words
- interior angle
- An angle on the inside of a shape, formed where two of its sides meet.
- unique triangle
- A triangle that is different in shape or size from every other triangle that fits the conditions.
Transcript
- [Instructor] How many unique triangles can be drawn with 110-degree angle, I'm assuming, and a 75-degree angle? I forgot to write angles here. But how many unique triangles can be drawn with 110-degree angle and a 75-degree angle? Pause the video and think about it.
Well, we know any triangle, the interior measurements of the interior, or the interior angle measurements, have to add up to 180 degrees. So if you just add up these two angles right over here, this is going to be 185 degrees. So there's not even space. There's not even an angle measurement that the third one can be that will add up to 180 degrees.
So there's no triangle that you could draw where you have one angle that is with 110 degrees, and another angle that is 75, so this is no triangle.
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