We know that <5 and <7 are supplementary. <7 and <9 are also supplementary because it is
given that <5 and <9 are supplementary.
given that <5 and <7 are supplementary. Now, it is also given that <7 and <9 are supplementary. To prove this statement, we need to show that the sum of the measures of <7 and <9 is equal to 180 degrees, which is the definition of supplementary angles.
Let x be the measure of <5.
Since <5 and <7 are supplementary, we have:
x + <7 = 180 degrees (Equation 1)
Let y be the measure of <7.
Since <7 and <9 are supplementary, we have:
y + <9 = 180 degrees (Equation 2)
Now, we need to solve the system of equations formed by Equation 1 and Equation 2.
From Equation 1, we have:
y = 180 - x
Substituting this into Equation 2, we get:
(180 - x) + <9 = 180 degrees
Simplifying, we have:
180 - x + <9 = 180 degrees
Rearranging the terms, we get:
<9 = x
This implies that <7 = 180 - x = 180 - <9
Hence, we have proved that <7 and <9 are supplementary angles.
To prove that <5 and <7 are supplementary, and <7 and <9 are supplementary, we need to use the definition of supplementary angles.
Supplementary angles are two angles whose sum is 180 degrees.
To show that <5 and <7 are supplementary:
1. Start by stating the given angles: <5 and <7.
2. Then, write down the equation for the sum of angles: <5 + <7 = 180 degrees.
3. Simplify the equation if possible: <5 + <7 = 180 degrees.
4. Solve the equation to find the value of <5 or <7 if given or required.
Similarly, to prove that <7 and <9 are supplementary:
1. Start by stating the given angles: <7 and <9.
2. Then, write down the equation for the sum of angles: <7 + <9 = 180 degrees.
3. Simplify the equation if possible: <7 + <9 = 180 degrees.
4. Solve the equation to find the value of <7 or <9 if given or required.
By following these steps, you can find the values of <5, <7, <9, or any other supplementary angles if given or required.