Complete the following paragraph proof. (You may use the choices more than once and you may not use all the choices)

Question

Given: <5 and <7 are supplementary. <7 and <9 are also supplementary

Prove: <5≅<9

We know that <5 and <7 are supplementary. <7 and <9 are also supplementary because it is

M<5 + m<7 =

and m< 7 + m<9 =

by definition of supplementary angles. Then, m<5 + m<7 = m<7 + m<9 by the

. Subtract m<7 from each side and you get m<5 = m<9. Then by the ​​​​​​​definition of congruence, <5 ≅

180 degrees
Symmetric property
<5
Addition property
<9
Given
Transitive property
Subtraction property
<7
90 degrees
Proven

Answer 1

We know that <5 and <7 are supplementary. <7 and <9 are also supplementary because it is given. We can write this as:

m<5 + m<7 = 180 degrees (definition of supplementary angles)
m<7 + m<9 = 180 degrees (definition of supplementary angles)

We can set these two equations equal to each other since they both equal 180 degrees:

m<5 + m<7 = m<7 + m<9

Now, we can subtract m<7 from each side of the equation to isolate m<5:

m<5 = m<9

By the definition of congruence, we can conclude that <5 is congruent to <9:

<5 ≅ <9.