Let's consider the given diagram, hypothesis, and thesis.
Given:& △ ABC, exterior ∠ BCD
Prove:& m∠ A+m∠ B=m∠ BCD
According to the Triangle Sum Theorem, the sum of the measures of the three interior angles of a triangle add to 180^(∘).
Triangle Sum Theorem
m∠ A+m∠ B+m∠ BCA=180^(∘)
If we look at the diagram, we can see that ∠ BCA and ∠ BCD form a linear pair. According to the Linear Pair Postulate, the measures of two angles that form a linear pair add to 180^(∘).
Linear Pair Postulate
m∠ BCD+m∠ BCA=180^(∘)
By the Transitive Property of Equality, if two expressions equal 180^(∘), then they are equal.
Transitive Property of Equality
m∠ BCD+m∠ BCA = m∠ A+m∠ B+m∠ BCA
By the Subtraction Property of Equality, we can subtract m∠ BCA from both sides to obtain an equivalent equation.
Subtraction Property of Equality
m∠ BCD = m∠ A+m∠ B
⇕
m∠ A+m∠ B=m∠ BCD
We can summarize our proof using a table.
