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The Triangle Sum Theorem is three angles in a triangle that all adds up to 180. It can be one right angle, one acute angle and one obtuse angle. It could also be one obtuse angle and two acute angles. It can be three acute angles also. It can't be all right angles or all obtuse angle or more than one because it exceed 180.
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Exterior Angle Theorem is two angles in the triangle that equals to the exterior angle outside of the triangle. It can be two acute angles equal to the obtuse angle outside, one acute and one obtuse angle to equal an obtuse angle, or two different acute angles equal to the acute angle outside. It can't be two obtuse equal to the outside obtuse angle, because it will be too much. It can't be one acute and one obtuse angle equal to the outside acute angle because one big angle plus an acute angle cannot be a smaller angle.
How to do each:
Triangle Sum Theorem*:
- Set up the equation: ∠ 1 +∠ 2 +∠ 3 = 180
- Substitute the values
- Solve for x
- Check: Once you plug x back in, all the angles measures must add up to 180.
Exterior Angle Theorem*:
- Set up the equation: ∠ 1 +∠ 2 = exterior angle.
- Substitute the values
- Solve for x
- Check: Once you plug x back in, all the interior angles measures must add up to 180.