In a triangle, the smallest angle is 36 degrees less than half the largest angle. The middle angle is 60 degrees more than the smallest angle. What is the measure of the largest angle?
2007-09-26 18:01:44 · 4 answers · asked by DoWHATiDO 3 in Science & Mathematics ➔ Mathematics
Call the angles S, M and L. We know:
S = L/2 - 36
M = S + 60
S + M + L = 180
Use the first and second equations to write M in terms of L:
M = S + 60 = (L/2 - 36) + 60 = L/2 + 24
So we have
(L/2 - 36) + (L/2 + 24) + L = 180
=> 2L - 12 = 180
=> L = 192/2 = 96°
M = L/2 + 24 = 48 + 24 = 72°
S = L/2 - 36 = 48 - 36 = 12°.
So the largest angle is 96° (and the other angles are 72° and 12°).
2007-09-26 18:09:30 · answer #1 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
Let x be smallest angle
Let y be middle angle
Let z be largest angle
x + y + z = 180
((1/2)z - 36) + ((1/2)z - 36 + 60) + z = 180
z -12 + z = 180
2z = 192
z = 96
Hence largest angle is 96 degrees
2007-09-27 01:09:31 · answer #2 · answered by tancy2411 4 · 0⤊ 0⤋
Let largest angle be a,
Let middle angle be b,
Let smallest angle by c,
c+36 = a/2
c = a/2 -36
b = c+60
b = a/2 - 36 + 60
b = a/2 +24
a+b+c = 180
a + a/2 + 24 + a/2 - 36 = 180
2a - 12 = 180
2a = 192
a = 96
The greatest angle is 96 degree.
2007-09-27 01:08:42 · answer #3 · answered by chingmenghang 3 · 0⤊ 0⤋
Just solve these 3 equations:
s + m + l = 180
s = 1/2l - 36
m = s + 60
The rest I'll leave to you :-)
2007-09-27 01:11:09 · answer #4 · answered by DannyM 1 · 0⤊ 0⤋