Algebra. System of Equations. Word Problems. Setting up the equation.?

Question

In a certain triangle, the measure of the second angle is 10 degrees more than three times the first. The thrid angle measure is equal to the sum of the measures of the other two. Find the measures of all three angles.

Lets say the first angle is x, the second angle is y, and the third angle is z. I think I have one equation figured out: y = 3X +10.

What are the other two?

Answer 1

you're on the right track:

first angle call x
second angle is y = 3x+ 10
third angle is z= x + y

we know that x + y + z = 180 (the 3 angles of a triangle added together equal 180 degrees)
now just use substitution:
x+ 3x + 10 + x + 3x + 10 = 180
8x + 20 = 180
8x = 160
x = 20

now we know x we can substitute in y=3x + 10
so y= 3 (20) + 10
y = 70

and z = x + y
so z = 20 + 70
z = 90

to check this is correct :
x + y + z = 180
20 + 70 + 90 = 180
180 = 180

done!

Answer 2

instead of in terms of x and y, put the equation in just x.
Let the first angle be x.
Second angle= 3x+10
Third angle = (3x+10) + x
So, third angle=4x+10
Since all the angles in a triangle add up to 180 degrees.
x + (3x+10) + (4x+10) = 180
8x + 20 =180
8x + 160
x = 20.
So, first angle = 20 degrees.
second angle = 3x+10 = 3*20 +10 = 70 degrees
third angle = 4*20 +10 = 90 degrees.
Hope it helps.

Answer 3

It is easier to keep everything in terms of the first angle.

1st angle = x
2nd angle = 3x +10
3rd angle = x + 3x + 10

All three angles in a triangle total 180 degrees so solve:

x + 3x + 10 + [x + 3x + 10] = 180 to find the first angle

I'll leave the rest to you!

Answer 4

Angle 1= 20 degrees, Angle 2= 70 degrees, Angle 3= 90 degrees. sorry if you don't like my answer

Answer 5

$30 VIP tickets= X $18 = 1/5X $10= 11/5X 10(11/5X)+ 18(1/5X) + 30(X) = 9500 22X+ 18/5X + 30X= 9500 278/5X=9500 278X= 47,500 X=171 $30 = 171 Tickets $18 = 34 Tickets $10 = 376 Tickets

Answer 6

x + y = z

x + y + z = 180

Answer 7

i think another one is z=3x squared + 10.