Question

If measure angle 3 equals (4x+5y), angle 4 = (10x+10y), and angle 5 = (6x-20y), find the value of x, the value of y, and the measure of angle 8.

Answer 1

So, from the picture, it looks like we have a set of interior opposite angles in angles 3 and 5. That means that if we add the measures of those angles together, we should get 180.
Angles 3 and 4 are adjacent on the same line, so their measures will also add up to 180.
So, we have
Angle 3 + Angle 5 = Angle 3 + Angle 4 = 180

Now, let's bring the variables into this.
14x+15y=10x-15y
4x = -30y
Now, we can substitute x for -30/4y, or -7.5y
10(-7.5y)-15y = 180
90y = 180
y = 2
And since 4x=30y, that means x=15.
Now, you can just plug the values of x and y into the equations for each angle.
Note that angle 4 is equal to angle 8, since they are corresponding angles. Or, we could use the fact that angle5 + angle8 = 180

Answer 2

Ok

Answer 3

i dont get it.

Answer 4

So we found that x is 15 and y is 2, right?
And we have the equations for all of the angles, using x and y, right?
So if we replace x with 15 and y with 2 in those equations, we'll find the measures of each of the angles

Answer 5

Dude? can you explain what Smokey said for the first part?

Answer 6

Lol what part are you confused on? *highlight and repost it*

Answer 7

when smokey replied after i posted the image

Answer 8

@dude ?

Answer 9

Do you know what opposite interior angles are?

Answer 10

yes

Answer 11

You know they add up to 180, right?

Answer 12

yes

Answer 13

What did you not get? xD
Do you know what adjacent means?

Answer 14

yes. i dont get the equations. how did he get up to 14x+15y=10x-15y
4x = -30y?

Answer 15

Smokey added angle 3 (4x+5y) and angle 4 (10x+10y)

to get 14x+15y

Because they add up to 180


Angle 3 and angle 5 were added because they are adjacent (AKA supplementary; they both add up to 180)

Since they both add up to 180, they should be the same

(Angle 3+4)=(Angle 3+5)
14x + 15y = 10x-15y

Answer 16

ok. then what.

Answer 17

4x=-30y?

Answer 18

They subtracted 15y on both sides

Answer 19

ok

Answer 20

wait. cant i do 4x+30y=180?

Answer 21

No, you already set them equal to each other, setting that equal to 180 is not correct because 4x+30y is not either equation

Answer 22

then i dont get it.

Answer 23

What 4x+30y is a modified version of it, they are not equal, you combined terms from 2 different equations, they can no longer be 180


What Smokey did was isolate x (by dividing by 4 on both sides)
\(4x=-30y\)
\(x=-\frac{30}{4}y=-7.5y\)

Answer 24

ok

Answer 25

Then they substitute it into (angle 3+5)

\(10(-7.5y)-15y = 180\)

Answer 26

wait. so angle 3+5 is what?

Answer 27

\(\color{#0cbb34}{\text{Originally Posted by}}\) @dude
Smokey added angle 3 (4x+5y) and angle 4 (10x+10y)

to get 14x+15y

Because they add up to 180


Angle 3 and angle 5 were added because they are adjacent (AKA supplementary; they both add up to 180)

Since they both add up to 180, they should be the same

(Angle 3+4)=(Angle 3+5)
14x + 15y = 10x-15y
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 28

ahhhhhhh. ok

Answer 29

-15y=105