Question

Given: < 1 and < 2 are right angles. Prove: < 1 = < 2

Answer 1

Statement.
(1). ∠1 is right angle & ∠2 is right angle

(2). ∠1 = ∠2

Reason
(1). Given

(2). Euclid’s Fourth Postulate states that all right angles are equal to one another.

Warning
This is assuming, that we only include Euclidean geometers.
This is because Euclidean geometry only recognise angles between straight lines.

So we have Non-Euclidean geometry for things that are not straight but this raises a question what is a straight line?

A general definition is (A curve is "straight' if tangent vectors stay tangent when parallel-transported along that curve)

Want more info

http://www.physics.ucc.ie/apeer/PY4112/Curvature.pdf

(Elementary Geometry from an Advance Standpoint, by Edwin Moise).