the sum of the three angles of any triangle is 180 degree. In a certain triangle, the second angle is 24 degree less than the sum of the other two angles, and the sum of the first and the second angles is 11/7 of the third angle. find the measure of each angle.

Question

anonymous · Answer

Well let:
 
a=first angle
b=second angle
c=third angle

from your post we can set up a system of equations:

(1) a+b+c = 180
(2) b = a+c -24
(3) a+b=11c/7

now we have to solve the system. substitution is the easiest way. 

substitute (2) into (1)

a+[a+c-24]+b+c=180
2a+2c = 180 + 24
2(a+c) = 204
a+c = 102

Now that you know this, plug this into (1)
 
a +b+c=180
b +(a+c) = 180
b + [102]=180
b = 180-102
b = 78

Now put this in equation (3)

a+b = 11/c/7
a+78 = 11c/7
a = 11c/7 -78

and throw it in (1)

a+b+c =180
11c/7-78 + 78 +c = 180
11c/7+7c/7 = 180
18c/7 = 180
c = 180*7/18
c = 70

Finally now that you know two of the angles:

a+b+c=180
a+78+70=180
a+148=180
a=180-148
a=32

So the angles are:
first:      32
second: 78
third:    70