Question

Find X,Y & all 4 angles

Answer 1

The angles measuring 4x and 5y measure: 3600/47

The other two angles measure: 4860/47

Explanation:

The angles measuring 4x and 5y are vertical angles. Vertical angles are congruent, so we have one equation: 4x = 5y.

The angles measuring 5y and 3x + 3y form a linear pair. Angles in a linear pair are supplementary, so their measures add up to 180 degrees. That gives us a second equation: 3x + 3y + 5y = 180, or simply 3x + 8y = 180.

We have a system of two equations in two unknowns, so we can solve for x and y.

4x = 5y

3x + 8y = 180

We will use the substitution method.

Solve the first equation for x: x = 5y/4

Substitute 5y/4 for x in the second equation.

3(5y/4) + 8y = 180

15y/4 + 8y = 180

15y + 32y = 720

47y = 720

y = 720/47

Substitute y with 720/47 in the first original equation and solve for x.

4x = 5y

4x = 5(720/47)

4x = 3600/47

x = 900/47

The angles measuring 4x and 5y measure: 4x = 4(900/47) = 3600/47

The other two angles measure: 3x + 3y = 3(900/47) + 3(720/47) = 2700/47 + 2160/47 =4860/47

Answer 2

x=900/47, y=720/47

4x=5y == 3600/47 (top and bottom angle values)

3x+3y == 4860/47 (left and right angle values)

If you want the values in mixed number form, reply back.

Step-by-step explanation:

You can set this up in many different ways.

First, the inverse angles are always equal, so 4x=5y

Additionally, 2 sets of angles are supplementary, meaning they add up to 180 degrees; they are 4x+3x+3y=180 and 5y+3x+3y=180; both are equal

You could simplify the above two equations to get 7x+3y=180 and 3x+8y=180, meaning that 7x+3y=3x+8y, and 4x=5y

This simplifies to y=4x/5

Additionally, you could add the equations, meaning that 10x+11y=360, and y=4x/5

This gives you the answer:

x=900/47 and y=720/47.

You could check this by plugging the values into the equation, and if you do the math (which, I know, is kind of painful), you get the supposed values, so hooray!