Angles that create a triangle always add up to 180.
To find sides that create triangles, we have to use the Triangle Inequality Theorem. It's where side A + B will <em>always</em> be greater than side C and B + C will always be greater than side A <em>and</em> A + C will always be greater than side B.
So let's check all of these answers and pick the one that's incorrect.
For a triangle to be "true", it must either have angle measures that total to 180 degrees or have two sides whose sum is greater than the third side.
For the first one, the angles total to 180 (10+25=35 and 145+35=180). This is a good triangle.
In the second one, the two shorter sides are 9 and 9. Adding these up, we get a sum of 18, and since this is greater than 15 (the third side), this triangle is also good.
The third triangle has angle measures that equal 175. Since it is less than 180 degrees, this is not a good triangle.
Finally for the fourth one, we see that the two shorter sides are 6 and 8. Their sum is 14, and since this is greater than 10, this is a good triangle.
So our third option is the one that cannot create a triangle.
