Question

given: ∠1 and ∠2 are supplementary, ∠2 & ∠3 are supplementary
prove: m∠3 = m∠1

statements	reasons
2. m∠3 + m∠2 = 180 m∠2 + m∠1 = 180	2.
3. m∠3 + m∠2 = m∠2 + m∠1	3. transitive property
4. m∠3 = m∠1	4.

addition property of equality subtraction property of equality
definition of congruence definition of supplementary angles
definition of complementary angles

Explanation:

Step1: Use the definition of supplementary angles

By the definition of supplementary angles, if two angles are supplementary, the sum of their measures is \(180^{\circ}\). So, since \(\angle1\) and \(\angle2\) are supplementary, \(m\angle1 + m\angle2=180^{\circ}\), and since \(\angle2\) and \(\angle3\) are supplementary, \(m\angle3 + m\angle2 = 180^{\circ}\).

Step2: Use the subtraction property of equality

We have \(m\angle3 + m\angle2=m\angle2 + m\angle1\) (from step1 and transitive property). Subtract \(m\angle2\) from both sides of the equation \(m\angle3 + m\angle2=m\angle2 + m\angle1\). According to the subtraction property of equality, if \(a + b=c + b\), then \(a=c\). So, \(m\angle3=m\angle1\).

Answer:

1. Definition of Supplementary Angles; 4. Subtraction Property of Equality