Question

in claim 1, she claims that ( mangle1 + mangle2 = 180^circ ) and ( mangle2 + mangle3 = 180^circ ) implies that ( mangle1 + mangle2 = mangle2 + mangle3 ).
in claim 2, she claims that ( mangle1 + mangle2 = mangle2 + mangle3 ) implies that ( mangle1 = mangle3 ).
which properties give the reasons for claim 1 and for claim 2?
a claim 1: transitive property of equality; claim 2: subtraction property of equality
b claim 1: addition property of equality; claim 2: subtraction property of equality
c claim 1: division property of equality; claim 2: addition property of equality
d claim 1: reflexive property of equality; claim 2: addition property of equality

Explanation:

Step1: Analyze Claim 1

Given \(m\angle1 + m\angle2=180^{\circ}\) and \(m\angle2 + m\angle3 = 180^{\circ}\). By the transitive property of equality (if \(a = b\) and \(b = c\), then \(a = c\)), since \(m\angle1 + m\angle2\) and \(m\angle2 + m\angle3\) both equal \(180^{\circ}\), we can say \(m\angle1 + m\angle2=m\angle2 + m\angle3\).

Step2: Analyze Claim 2

Given \(m\angle1 + m\angle2=m\angle2 + m\angle3\). Subtract \(m\angle2\) from both sides of the equation. By the subtraction property of equality (if \(a=b\), then \(a - c=b - c\)), we get \(m\angle1=m\angle3\).

Answer:

A. Claim 1: transitive property of equality; Claim 2: subtraction property of equality