Question

Which labeled angle has the greatest measure?

Answer 1

I think it's Angle 2.

Answer 2

Wait, if the 3 is on the outside, that means the angle is on the outside?

Answer 3

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles. Angles 1 and 2 are the remote (far away) angles to exterior angle 3.

Answer 4

Yes

Answer 5

Not only that, but m<3 = m<1 + m<2, so which one must be the largest?

Answer 6

So you're saying 3 isn't the largest?

Answer 7

Geometry problems usually do not involve looking at a figure and concluding that since one angle looks larger, it must be larger. Drawings in geometry problems are usually not drawn to scale. You need to use your knowledge of geometry to come to conclusions.

Answer 8

I just stated that m<3 = m<1 + m<2. How did I imply that m<3 is not the largest?

Answer 9

Oh. I thought that meant Angle 1 or Angle 2 had to be the largest, nevermind.

Answer 10

You are correct when you realized that <3 is an exterior angle. Angle 3 must be the largest of the three angles bec it is as large as angles 1 and 2 put together.

Answer 11

The statement I quoted above, "The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles." is a theorem. This is how you prove things in geomtery.