Question

What reason can be used to complete this proof?

m∠1=m∠3 because ∠1≅∠3.
m∠1+m∠2=m∠CXB and m∠2+m∠3=m∠AXD _________.
A. m∠1+m∠2=m∠AXD because you can substitute m∠1 for m∠3.
B. m∠CXB=m∠AXD by the transitive property of equality.
C. m∠1+m∠2=m∠CXB because that is given information.
D. m∠1+m∠2=m∠CXB because you can measure them with a protractor.

Answer 1

The correct reason to complete the proof about angle measures is B. m∠CXB = m∠AXD by the transitive property of equality, as we can substitute m∠1 for m∠3.

Step-by-step explanation:

The question pertains to a geometric proof regarding angles and their measures. The correct reason to complete the proof statement that given m∠1 + m∠2 = m∠CXB and m∠2 + m∠3 = m∠AXD, is B. m∠CXB = m∠AXD by the transitive property of equality. This is because we can substitute m∠1 for m∠3 as it is given that ∠1 ≅ ∠3. By adding m∠1 + m∠2 on one side and m∠2 + m∠3 on the other, and knowing both are equal to their respective angles m∠CXB and m∠AXD, we show that m∠CXB is equal to m∠AXD.