Understanding Angle Proofs: How to Identify and Solve for Equal Angles

[Miike012]

Quick angle question...

I am going over the sum of two angles proof... and I am confused about one thing..( my geometry isn't that great) can some one tell me how to two red angles are the same...? thank you.
I posted a pick ...

 

[Mark44]

The two triangles the angles are in are right triangles, right?
At the intersection of the vertical line and the lower of the two slanted lines coming out of the origin, there's one angle of the upper right triangle, and another angle of the lower right triangle. These angles are opposite angles, which means they are equal. So we have two triangles, both with a 90°, and each one has an angle that's equal to an angle in the other triangle. That means that the remaining angles of the two triangles (the ones you're asking about) have to be equal as well.

 

[Fewmet]

I am going over the sum of two angles proof... and I am confused about one thing..( my geometry isn't that great) can some one tell me how to two red angles are the same...? thank you.
I posted a pick ...

Call the lower left vertex A. Let the right angle to the right be B, and the angle above C. Make the red angle above that D and the other right angle E.

Angle BCA is the same as DCE (they are reflex angles). Triangle ABC and DCE are both right angles. That gives two triangles with two angles in common, so the third angles (the red angles) must be equal.

(Sorry about the duplication. In the time I tried to post a lettered diagram, Mark 44 got the answer in.)