Answer:
45° and 135°
Step-by-step explanation:
let one angle be "x" and the other be "y"
Angles which are supplementary total to 180°. This can be represented with the equation:
x + y = 180
If angle "x" is a third of angle "y", the situation is represented with this equation:
(1/3)x = y
Since fractions are difficult to work with, multiply the whole equation by 3.
(1/3)x = y <= X 3
x = 3y
Use the equations x+y=180 and x=3y.
You can substitute x=3y into x+y=180.
x + y = 180
(3y) + y = 180 <=combine like terms
4y = 180 <=isolate y by dividing both sides by 4
y = 45
Substitute y=45 itno the equation x+y=180 to find x.
x + y = 180
x + 45 = 180 <=isolate x by subtracting 45 from both sides
x = 135
Therefore the angles are 45° and 135°.
Answer:
z = 4
y = -1
x = 2
Step-by-step explanation:
x - y = 3
Therefore => x = 3 + y
y + 2z =7
Therefore => y= 7 - 2z
We have the equation :
2x + 3y + 4z = 17
2(3 + y) + 3(7 - 2z) + 4z = 17
6 + 2y + 21 - 6z +4z = 17
2(7 -2z) - 2z + 27 = 17
14 - 4z - 2z + 27 = 17
-6z + 41 = 17
-6z = -24
z = 4
Solve for x by simplifying both sides of the equation, then isolating the variable.
x = 4
4x + 3y = 54 (1)
3x + 9y = 108 (2)
Multiply (1) by (-3)
-12x - 9y = -162
3x + 9y = 108
---------------------add
-9x = -54
x = 6
plug x = 6 into (1) to find y
4(6) + 3y = 54
24 + 3y = 54
3y = 30
y = 10
Answer
(6 , 10)
Hope it helps.
