If m = 49°, m = 2x
+ 10, and m = 4x – 15,
find the degree measure of
and . The diagram
is not to scale.
(1 point)
m = 21°; m
= 28°
m = 18°; m
= 31°
m = 28°; m
= 21°
m = 31°; m
= 18°
To solve this problem, we need to set up an equation using the given information.
We are told that m = 49° and m = 2x + 10. We can set these equal to each other to get:
49 = 2x + 10
We can solve this equation to find the value of x:
49 - 10 = 2x
39 = 2x
x = 19.5
We are also told that m = 49° and m = 4x - 15. We can set these equal to each other to get:
49 = 4x - 15
We can solve this equation to find the value of x:
49 + 15 = 4x
64 = 4x
x = 16
Now that we have the value of x, we can substitute it back into the equation m = 2x + 10 to find the degree measure of m:
m = 2(19.5) + 10
m = 39 + 10
m = 49
Therefore, the degree measure of m is 49°.
We can also substitute the value of x into the equation m = 4x - 15 to find the degree measure of m:
m = 4(16) - 15
m = 64 - 15
m = 49
Therefore, the degree measure of m is 49°.
In summary, the degree measure of m is 49° and m is also equal to 49°. Therefore, the degree measure of m is 49° and m is also equal to 49°.