Use the identity (x+y)(x−y)=x^2−y^2 to find the difference of two numbers if the sum of the numbers is 12 and the difference of the squares of the numbers is 48.

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1. ∠1 is complementary to ∠2 and ∠3 is complementary to ∠2. subtraction property of equality 2. m∠1 + m∠2 = 90 and m∠3 + m∠2 = 90 substitution 3. m∠1 + m∠2 = m∠3 + m∠2 definition of complementary 4. m∠1 = m∠3 given