Answer:
Step-by-step explanation:
We know that the sum of the angles in a triangle is equal to 180, so we can set up the following equation:
[tex]X + Y + Z = 180[/tex]
From the problem statement, we can also set up the following two equations:
[tex]X = 8(Y + Z)[/tex]
[tex]Y = 3Z[/tex]
Substituting the last equation into the second, we get the following:
[tex]X = 8(3Z + Z)[/tex]
[tex]X = 8(4Z)[/tex]
[tex]X = 32Z[/tex]
Substituting the last two equations into the first, we get the following:
[tex]32Z + 3Z + Z = 180[/tex]
[tex]36Z = 180[/tex]
[tex]Z = 5[/tex]
We can then plug this number into the previous equations:
[tex]Y = 3Z[/tex]
[tex]Y = 15[/tex]
and
[tex]X = 32Z[/tex]
[tex]X = 160[/tex]
