fill in the blanks please
We know that <5 and <7 are supplementary. <7 and <9 are also supplementary because it is (BLANK) area m<5 + m<7 = (BLANK) area and m< 7 + m<9 = (BLANK) area, by definition of supplementary angles. Then, m<5 + m<7 = m<7 + m<9 by the (BLANK) area. Subtract m<7 from each side and you get m<5 = m<9. Then by the definition of congruence, <5 ≅ (BLANK)
We know that <5 and <7 are supplementary. <7 and <9 are also supplementary because it is a known fact that the sum of the measures of supplementary angles is equal to 180 degrees by definition of supplementary angles. Then, m<5 + m<7 = 180 degrees and m<7 + m<9 = 180 degrees, by definition of supplementary angles. By the Transitive Property, we can conclude that m<5 + m<7 = m<7 + m<9. Subtracting m<7 from each side, we get m<5 = m<9. Then, by the definition of congruence, <5 ≅ <9.
We know that <5 and <7 are supplementary. <7 and <9 are also supplementary because it is (given) area m<5 + m<7 = 180 degrees by definition of supplementary angles. Then, m<7 + m<9 = 180 degrees, by definition of supplementary angles. Then, m<5 + m<7 = m<7 + m<9 by the transitive property. Subtract m<7 from each side and you get m<5 = m<9. Then by the definition of congruence, <5 ≅ <9.
We know that <5 and <7 are supplementary. To fill in the blanks, let's break down the given information and the steps mentioned.
Supplementary angles are defined as two angles that add up to 180 degrees. So, we can write the equation:
m<5 + m<7 = 180° (Equation 1)
Similarly, <7 and <9 are also supplementary. We can write the equation:
m<7 + m<9 = 180° (Equation 2)
The question asks us to fill in the blanks based on these equations and other given information. Here's a step-by-step explanation:
1. By the definition of supplementary angles, the sum of the measures of angles forms a straight line, which is 180 degrees. Therefore, the first blank can be filled with "equal" and the second and third blanks can be filled with "180°".
2. Using Equation 1 and Equation 2, we have:
m<5 + m<7 = 180° (Equation 1)
m<7 + m<9 = 180° (Equation 2)
3. By the transitive property of equality, if two things are equal to the same thing, they are equal to each other. Therefore, we can say that:
m<5 + m<7 = m<7 + m<9
4. Subtracting m<7 from both sides of the equation, we get:
m<5 = m<9
5. Finally, using the definition of congruence, which states that if two angles have the same measure, they are congruent, we can fill in the last blank with "<9".
So, to summarize:
We know that <5 and <7 are supplementary. <7 and <9 are also supplementary because it is equal area m<5 + m<7 = 180°, and m<7 + m<9 = 180°, by definition of supplementary angles. Then, m<5 + m<7 = m<7 + m<9 by the transitive property of equality. Subtract m<7 from each side and you get m<5 = m<9. Then by the definition of congruence, <5 ≅ <9.