We know that <5 and <7 are supplementary. <7 and <9 are also supplementary because it is
given that <5 and <7 are supplementary and <7 and <9 are also supplementary. This means that the sum of the measures of <5 and <7 is equal to 180 degrees, and the sum of the measures of <7 and <9 is also equal to 180 degrees.
Supplementary angles are angles that add up to 180 degrees. In this case, since <5 and <7 are supplementary, their measures must add up to 180 degrees. Similarly, since <7 and <9 are supplementary, their measures must also add up to 180 degrees.
So, we can conclude that <5 + <7 = 180 degrees and <7 + <9 = 180 degrees.
given that angles <5 and <7 are supplementary, and angles <7 and <9 are also supplementary. We can conclude that angle <5 and angle <9 are also supplementary.
This is based on the property that if two angles are each supplementary to a third angle, then they are supplementary to each other.
given that <5 and <7 are supplementary. To prove that <7 and <9 are supplementary, we can use the Transitive Property.
The Transitive Property states that if two angles are each supplementary to a third angle, then they are supplementary to each other.
So, to prove that <7 and <9 are supplementary, we first need to prove that <5 and <9 are each supplementary to a third angle. Let's call this third angle <A.
Given that <5 and <7 are supplementary, we can say that:
<5 + <7 = 180°
Now, to prove that <5 and <9 are each supplementary to angle <A, we can say that:
<5 + <A = 180° ......(1)
<9 + <A = 180° ......(2)
From equation (1), we can isolate <A:
<A = 180° - <5
Substituting this value of <A into equation (2), we get:
<9 + (180° - <5) = 180°
Simplifying this equation, we have:
180° - <5 + <9 = 180°
Rearranging terms, we get:
<9 - <5 = 0°
Which then leads to:
<9 = <5
Now, we can conclude that <5 and <9 are supplementary to angle <A. Therefore, by the Transitive Property, we can say that <7 and <9 are also supplementary.
This proof shows that <7 and <9 are supplementary angles based on the given information.