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I need help on the following geography question. Please HELP

I need help on the following geography question. Please HELP-example-1

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By definition of linear pair and algebra properties we find that m ∠ 2 ≅ m ∠ 3.

How to prove a feature of a geometric system

In this problem we must determine the existence of a linear pair consisting in a ray and two semirrays, there is a condition: m ∠ 1 + m ∠ 3 = 180º. Linear pairs are two angles such that sum of such angles equals 180º:

Step 1: Assumptions.

m ∠ 1 + m ∠ 3 = 180º

Step 2: Definition of linear pair.

m ∠ 1 + m ∠ 2 = 180º

Step 3: Transitive property.

m ∠ 1 + m ∠ 2 = m ∠ 1 + m ∠ 3

Step 4: Compatibility with addition / Commutative, associative and modultative properties / Existence of additive inverse.

m ∠ 2 = m ∠ 3

Step 5: Definition of congruence.

m ∠ 2 ≅ m ∠ 3

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