Exercise 22 Page 490

We are told that ∠ 3 and ∠ 2 are complementary angles and that the measures of ∠ 1 and ∠ 2 add to 90^(∘). We want to prove that ∠ 3 and ∠ 1 are congruent angles. To do so, we will do a Flowchart Proof. Let's write the given information!

Since ∠3 and ∠2 are complementary angles, the sum of their measures is 90^(∘).

Using the Transitive Property of Equality, we can equate m∠ 3 + m∠ 2 to m∠ 1 + m∠ 2.

By the Subtraction Property of Equality, if we subtract m∠ 2 from both sides of the last equation, we can conclude that m∠ 3 = m∠ 1.

Finally, by the definition of congruent angles, we know that ∠3 is congruent to ∠ 1.

Therefore, ∠3 and ∠ 1 are congruent angles. The proof is complete.