Angel M and Angel N are supplementary angles. If Angel M is nine more than one half Angel N, what are the measures of the angels?
Angels can't be measured.
m+n = 180
m = 9 + .5n
so
9 + .5 n + n = 180
1.5 n = 171
n = 114
m = 180-114
I forgot to mention that.
To solve this problem, let's assume the measure of Angel N is x degrees.
According to the problem statement, Angel M is nine more than half of Angel N. We can express this mathematically as:
Angel M = (1/2) * Angel N + 9
Since Angel M and Angel N are supplementary angles, their sum is 180 degrees:
Angel M + Angel N = 180
Now, substitute the expression for Angel M from the first equation into the second equation:
((1/2) * Angel N) + 9 + Angel N = 180
To solve for Angel N, combine like terms:
(3/2) * Angel N + 9 = 180
Subtract 9 from both sides:
(3/2) * Angel N = 171
To isolate Angel N, divide both sides by (3/2):
Angel N = (171) / (3/2)
Simplify the right side:
Angel N = 114
Now, substitute the value of Angel N back into the first equation to find Angel M:
Angel M = (1/2) * 114 + 9
Simplify:
Angel M = 57 + 9
Angel M = 66
Therefore, Angel M measures 66 degrees, and Angel N measures 114 degrees.