Final answer:
The question likely pertains to geometry and the properties of angles or triangles. A specific answer cannot be provided due to typos and lack of context. Typically, geometric proofs involve the principle that the sum of interior angles in a triangle is 180 degrees.
Step-by-step explanation:
The question appears to be asking for enough information to prove an equation or a theorem related to geometry, probably involving angles or triangles, as it mentions angles summing up to 180 degrees which is a characteristic of the interior angles of a triangle. However, the question seems incomplete or contains typographical errors that make it difficult to provide a definitive answer.
One fundamental principle in geometry is that the sum of the interior angles of a triangle is always 180 degrees. This fact is frequently used to solve various problems and to prove theorems or other geometric statements. For example, if you know the measure of two angles in a triangle, you can always find the third.
Without further context or clarification of the specific problem at hand, any effort to provide a step-by-step explanation would be speculative. The provided reference information in the question, such as "23 + 11 = 34", "angles are defined as positive", and calculating probabilities like "P(R) == .5", suggests that the question might involve a combination of geometry, angle measurement, and perhaps probability or calculation involving angles.