if m<1 = 60 degrees, then m<3 + m<5 = what?
|
\2|
1 \| 3
------- | ------
6 |\ 4
|5\
|
what is the transitive property of angle congruence?
transitive: A≅B and B≅C ==> A≅C
No idea what the diagram shows.
m<1 = 76 degrees THEN M<3=
Find m<2
To find the value of m<3 + m<5, we need to determine the measure of angle <3 and <5 first.
From the diagram, we can see that angles <1 and <2 are vertical angles and are therefore congruent. So, m<2 = m<1 = 60 degrees.
The transitive property of angle congruence states that if two angles are congruent to the same angle (or to congruent angles), then they are congruent to each other. In other words, if m<1 = m<2 and m<1 = 60 degrees, then m<2 = 60 degrees as well.
Now that we know m<2 = 60 degrees, we can use the fact that angles <2, <3, <4, and <5 form a straight line. A straight line measures 180 degrees, so the sum of these angles is 180 degrees.
m<2 + m<3 + m<4 + m<5 = 180 degrees
Since m<2 = 60 degrees, we can substitute the value in:
60 + m<3 + m<4 + m<5 = 180 degrees
Now, we want to find the value of m<3 + m<5:
m<3 + m<5 = 180 degrees - m<2 - m<4
However, we don't know the value of m<4. To find it, we can use the fact that angles <4 and <5 are vertical angles, so they are congruent. Therefore, m<4 = m<5.
Now we can rewrite the equation:
m<3 + m<5 = 180 degrees - m<2 - m<4
= 180 degrees - 60 degrees - m<5
To solve for m<5, we bring all the terms involving m<5 to one side of the equation:
m<3 + m<5 + m<5 = 180 degrees - 60 degrees
2m<5 = 120 degrees
Finally, we can solve for m<5:
m<5 = 120 degrees / 2
= 60 degrees
Now we have the value of m<5, we can substitute it back into the equation to find m<3 + m<5:
m<3 + 60 = 180 degrees - 60 degrees
m<3 + 60 = 120 degrees
Subtracting 60 from both sides:
m<3 = 60 degrees
Therefore, m<3 + m<5 = 60 degrees + 60 degrees = 120 degrees.