Before making a flow proof, let's consider a triangle △ XYZ and the exterior angle corresponding to Y.
From the diagram we have that ∠ 1 and ∠ 2 are supplementary. Then, m∠ 1 + m∠ 2 =180^(∘), and so m∠ 1 = 180^(∘)-m∠ 2. Also, by applying the Triangle Angle-Sum Theorem we can set the equation below.
m∠ X + m∠ 2 + m∠ Z = 180^(∘)
⇓
m∠ X + m∠ Z = 180^(∘) - m∠ 2
By equating this equation with the one we wrote above we obtain the desired result.
m∠ 1 = m∠ X + m∠ Z
Flow Proof
Let's summarize the proof above in the following flow chart.
