Answer:
26,72,82
Step-by-step explanation:
This question is solved by a system of equations. We have that:
x is the first angle.
y is the second angle.
z is the third angle.
The sum of the measures of the angles of a triangle is 180.
This means that, x + y + z = 180 -> Eq 1
Now,
The second angle measure 10º more than twice the first,
=> y = 2(x + 10) = 2x + 20
The third angle measures 10° more than the second,
=> z = y + 10 = 2(x + 10) + 10 = 2x + 20 + 10 = 2x + 30
Equation(Substituting values in Eq 1) :-
=> x + (2x + 20) + (2x + 30) = 180
=> x + 2x + 20 + 2x + 30 = 180
=> x + 2x + 2x + 20 + 30 = 180
=> 5x + 50 = 180
=> 5x = 130
=> x = 26
Therefore,
x = 26
y = 2(26) + 20 = 72
z = 2(26) + 30 = 82
