Respuesta :
60,47,73
Step-by-step explanation:
Let the first angle be [tex]a[/tex] degrees
Let the second angle be [tex]b[/tex] degrees
Let the third angle be [tex]c[/tex] degrees
It is given that sum of angles is [tex]180[/tex] degrees.
so,[tex]a+b+c=180[/tex] ...(i)
It is given that sum of the measures of the second and third angles is two times the measure of the first angle.
[tex]b+c=2\times a[/tex] ...(ii)
It is given that the third angle is 26 more than the second.
[tex]c=26+b[/tex] ...(iii)
using (ii) and (iii),
[tex]b+b+26=2a[/tex]
[tex]b+13=a[/tex]
using (i),(ii) and (iii),
[tex]a+b+c=a+a-13+26+b=a+a-13+26+a-13=3a[/tex]
[tex]3a=180[/tex]
[tex]a=60[/tex]
[tex]b=a-13=60-13=47[/tex]
[tex]c=26+b=26+47=73[/tex]
Answer:
(X=60,Y=47,Z=73)
Step-by-step explanation:Start by translating the given information into a system of equations. The sum of the measures of the angles is 180, so we have
x+y+z=180
The sum of the measures of the second and third angles is two times the measure of the first angle, so
y+z−2x+y+z=2=0
The third angle is 26 more than the second, so
z−y+z=y+26=26
Therefore, we have the system of equations
x+y+z=180−2x+y+z=0−y+z=26(1)(2)(3)
Use equations (1) and (2) to find x by eliminating y and z. Multiply equation (2) by −1, and then add to equation (1) to eliminate y and z.
x+y+z2x−y−z3xx=180=0=180=60(4)
Use equations (1) and (3) to eliminate z. Multiply equation (3) by −1, and then add to equation (1) to eliminate z.
x+y+zy−zx+2y=180=−26=154(5)
Substitute x=60 into equation (5) to find
x+2y(60)+2y2yy=154=154=94=47
Now we can substitute x=60 and y=47 into equation (1) to find
x+y+z(60)+(47)+zz+107z=180=180=180=73
The solution is therefore (60,47,73).
