Question

given: ∠1 and ∠2 a linear pair; ∠2, ∠3, and ∠4 supplementary; prove: m∠1 = m∠3 + m∠4 statements reasons 1. ∠1 and ∠2 a linear pair; ∠2, ∠3, and ∠4 supplementary; 1. given 2. 2. supplement theorem 3. 3. definition of supplementary ∠s 4. m∠2 + m∠3 + m∠4 = 180° 4. 5. m∠1 + m∠2 = m∠2 + m∠3 + m∠4 5. 6. m∠1 = m∠3 + m∠4 6.

Explanation:

Step1: Recall linear - pair property

Since ∠1 and ∠2 are a linear pair, by the Supplement Theorem, ∠1 and ∠2 are supplementary, so \(m\angle1 + m\angle2=180^{\circ}\).

Step2: Define supplementary angles

Because ∠2, ∠3, and ∠4 are supplementary, by the definition of supplementary angles, \(m\angle2 + m\angle3 + m\angle4 = 180^{\circ}\).

Step3: Substitute equal - values

Since \(m\angle1 + m\angle2=180^{\circ}\) and \(m\angle2 + m\angle3 + m\angle4 = 180^{\circ}\), we can substitute to get \(m\angle1 + m\angle2=m\angle2 + m\angle3 + m\angle4\).

Step4: Use subtraction property of equality

Subtract \(m\angle2\) from both sides of the equation \(m\angle1 + m\angle2=m\angle2 + m\angle3 + m\angle4\). We get \(m\angle1=m\angle3 + m\angle4\).

Answer:

Statements	Reasons
2. \(m\angle1 + m\angle2 = 180^{\circ}\)	2. Supplement Theorem
3. \(m\angle2 + m\angle3 + m\angle4=180^{\circ}\)	3. Definition of Supplementary ∠'s
4. \(m\angle2 + m\angle3 + m\angle4 = 180^{\circ}\)	4. Definition of Supplementary ∠'s
5. \(m\angle1 + m\angle2=m\angle2 + m\angle3 + m\angle4\)	5. Substitution Property of Equality
6. \(m\angle1=m\angle3 + m\angle4\)	6. Subtraction Property of Equality