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Complete the two-column proof. Given: <2 = <4, m<2 = 110 Proof: m<3 = 70 <2 = <4, m<2 = 110 Given m<2 = m<4 Definition of congruent angles m<4 = 110 b._______ <3 and <4 are a linear pair Definition of a linear pair(shown in diagram) <3 and <4 are supplementary Linear Pair postulate m<3 + m<4 = 180 c.________ m<3 = 70 d._______

Tara Andrews

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Ronald Miller on February 10, 2019

The correct answers are: (b) substitution; c) definition of supplementary angles; (d) the subtraction property of equality. Explanation: We are given that ∠2 = ∠4 and m∠2 = 110°. We can replace the measure of ∠4 instead of m∠2 are congruent, and get m∠4 = 110°, with the reason for the replacement. Then we have that ∠3 and ∠4 are a linear pair from a diagram, and that ∠3 and ∠4 are complementary with the reason of be of the linear pair postulate. Since they are complementary, this means that m∠3 + m∠4 = 180°, with the reason of be of the definition of supplementary angles. Once we have this, we know that m∠4 = 110°; this gives us that m∠3+110°=180°. Then, we subtract 110 from both sides: m∠3 + 110°-110° = 180°-110°This gives us that m∠3 = 70°, with the reason for the subtraction property of equality.


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