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McGraw Hill Integrated II, 2012 View details

4. Proving Angle Relationships

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Exercise 20 Page 305

Look for angles that form a linear pair.

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Let's start by noticing that ∠ 1 and ∠ 2, as well as ∠ 3 and ∠ 4, form a linear pair.

Using the Supplement Theorem, we get the following two relations. m∠ 1 + m∠ 2 &= 180 m∠ 3 + m∠ 4 &= 180 By adding these two equations we obtain what we wanted to prove. m∠ 1 + m∠ 2 + m∠ 3 + m∠ 4 = 360 Notice that ∠ 1 and ∠ 4, as well as ∠ 2 and ∠ 3, also form a linear pair.