Answer:
52degrees
Step-by-step explanation:
Let the measure of the largest angle be x
middle angle be y
smallest angle be z
Since the sum of angle in a triangle is 180 degrees, hence;
x + y + z = 180 .... 1
If the measure of the largest angle is 32 less than 3 times the smallest angle, then;
x = 3z - 32
3z = x+ 32
z = x+32/3 ..... 2
If he measure of the middle angle is 8 more than half the measure of the largest angle, then;
y = x/2 + 8 .... 3
Substitute 2 and 3 into 1;
x + x/2 + 8 + (x+32)/3 = 180
multiply through by 6
6x + 3x + 48 + 2(x+32) = 1080
9x + 48 + 2x + 64 = 1080
11x + 112 = 1080
11x = 1080-112
11x = 968
x = 968/11
x = 88 degrees
Get the middle angle y;
Since y = x/2 + 8
y = 88/2 + 8
y = 44 + 8
y = 52 degrees
Hence the measure of the middle angle is 52degrees
