Â=2¼n°+½m°, B=2n°-⅖m°, C=2m°, find m, n and the sizes of  and B
To find m and n, we can set up a system of equations using the given information:
From the first equation Â=2¼n°+½m°, we can write this as  = 9/4n + 1/2m.
From the second equation B=2n°-⅖m°, we can write this as B = 2n - 2/5m.
Given that  and B are supplementary angles, we know that  + B = 180°. So we can set up the equation:
(9/4n + 1/2m) + (2n - 2/5m) = 180
Multiplying out the terms and simplifying, we get:
9n/4 + n + m/2 - 2m/5 = 180
36n + 20n + 10m - 8m = 1440
56n + 2m = 1440
Given that C = 2m°, we can set up another equation C = 2m = 180, solving for m:
2m = 180
m = 90
Now that we have found the value of m, we can substitute it back into the equation 56n + 2m = 1440:
56n + 2(90) = 1440
56n + 180 = 1440
56n = 1260
n = 22.5
So, m = 90 and n = 22.5.
To find the sizes of  and B, we can substitute the values of m and n back into the equations  = 9/4n + 1/2m and B = 2n - 2/5m:
 = 9/4(22.5) + 1/2(90) = 20.25 + 45 = 65.25 degrees
B = 2(22.5) - 2/5(90) = 45 - 36 = 9 degrees
Therefore, Â is 65.25 degrees and B is 9 degrees.