Â=2¼n°+½m°, B=2n°-⅖m°, C=2m°, find m, n and the sizes of  and B

Answer 1

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.