Question

the second angle of an architects triangle is three times as large as the first. the third angle is 45 degree less than the sum of the other two angles find the measure of each angle

Answer 1

Call 'em a,b,c (First, second and third)
b=3a
c=a+b-45
And since for any triangle, a+b+c=180, you can substitute as
a+3a+a+3a-45=180 This will give you a=28.12...
since b=3a, b=84.37...
and finally, since c=a+b-45, c=67.49

Answer 2

angles x y z

y = 3x.......................(1)
z = (x+y) - 45............(2)
x + y + z = 180.........(3)

from (3): x+y = 180-z
sub this is (2)
z = 180 - z - 45
z = 135/2 = 67.5 degree
sub for z in (2)
67.5 = x + y - 45
x+y = 112.5
now y = 3x
so 4x = 112.5
and x = 28.125 degress
and finally y = 180-(28.125+ 67.5) = 84.375

Answer 3

thanks