What is the proof for angle equality?

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I've been searching over the internet and geometry books for the proof of the relationship of these two angles but I couldn't find one. Can you tell me the "how" and "why" of their equality. thanks and regards!
 

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Use the fact that when two lines intersect, opposite angles are equal. The result then follows.
 
Check post #5.

http://mathhelpboards.com/trigonometry-12/equality-angles-11593.html

"There is a theorem saying that two angles whose sides are mutually perpendicular are equal. "
 

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