Question

Can anyone help me with this problem, I need an explanation how to solve these step by step:
∠ RQS and ∠ TQS are vertical angles where m∠ RQS = 3(x + 7) and m∠ TQS = 4x + 15.

Answer 1

@ranga please help?

Answer 2

Can you post the sketch?

Answer 3

there is no sketch that's the thing all I need to do is solve for x but this equation is a bit hard...I know that the answer of RQS and TQS supposedly eqaul

Answer 4

Yes vertical angles are equal. But how did they letter them?
For instance, here are two vertical angles:

Answer 5

Here RQS and TQS are not vertical angles. They are supplementary angles.
RQS and TQU are vertical angles.

Answer 6

Can you post the problem exactly as it appears in the book? Perhaps a snap shot?

Answer 7

that's exactly how it is

Answer 8

IDK how they can form vertical angels with RQS and TQS.

But we will go with that. The vertical angles are equal.

Therefore, 3(x + 7) = 4x + 5
Distribute on the left.

Answer 9

4x+x=7+5?

Answer 10

No. Distribute means: 3(x+7) = 3x + 21 (each term inside the parenthesis has to be multiplied by the outside term.

Answer 11

So 3x + 21 = 4x + 5
subtract 3x from both sides

Answer 12

3x + 21 = 4x + 5
subtract 3x from both sides
21 = x + 5
subtract 5 from both sides
16 = x
So x = 16.

Answer 13

oh I finally realized how you did that! Thank you so much I think I how how to do the rest! Thank you again

Answer 14

you are very welcome.

Answer 15

Just noticed a typo. The right hand side is 4x + 15 not 4x + 5.
3x + 21 = 4x + 15
subtract 3x from both sides
21 = x + 15
subtract 15 from both sides
6 = x
So x = 6

Answer 16

Oh thank you for letting me know, I was doing english now and didn't go to math yet so I guess Its not too late! thank you again you've done a lot of help for me

Answer 17

@cwrw238 please help I figired the answer but it seems that the answer does not add up to 180 as if its supposed to be supplementary angle?

Answer 18

I raised the question before. In the sketch you can see RQS and TQS are supplementary angles not vertical angles. But the problem says they are vertical angles. I think the problem is wrong.

But here is the solution if we correct the problem and change vertical angles to supplementary angles. Do you have the answer to the problem?

Answer 19

If we assume RQS and TQS are supplementary, then RQS + TQS = 180 degrees
3(x+7) + 4x+15 = 180
3x + 21 + 4x + 15 = 180
7x + 36 = 180
7x = 180 - 36 = 144
x = 20.6 degrees

Answer 20

Do you have the answer to this problem?

Answer 21

hold on my connection was lost so let me solve it

Answer 22

the answer is 186.2
what I did is
3*(20.6+7)=82.8
4*20.6+21=103.4
and 103.4+82.8=186.2

Answer 23

4*20.6+21 should be 4*20.6 + 15 = 97.4

Answer 24

oh crap lol sorry I had tons of things on my mind and I misread it omg sorry so I get it like this
97.4+103.4=200? thats a bit over 180?

Answer 25

Here is the full solution. The problem is definitely worded wrong.

If we assume they are vertical angles, then vertical angles are equal.
Earlier we solved for x and got x = 6
RQS = 3(x + 7) = 3(6 + 7) = 3*13 = 39
TQS = 4x + 15 = 4*6 + 15 = 39

We assumed they are vertical angles and we just verified RQS = TQS = 39

Answer 26

Now we will assume they are supplementary angles. Therefore they add to 180 degrees
Earlier we solved for x and x = 20.6 degrees (rounded to first decimal)

RQS = 3(x + 7) = 3(20.6 + 7) = 3*27.6 = 82.8
TQS = 4x + 15 = 4*20.6 + 15 = 97.4

RQS + TQS = 82.8 + 97.4 = 180.2 (rounded off to 180)

We assumed they are supplementary angles and we just verified RQS + TQS = 180

Answer 27

I was about to type the exact thing, I just solved it and answer was 180.2 lol i guess I'm catching up fast thank you again for the help

Answer 28

With the second assumption that they are supplementary angles we get a decimal value for x (x = 20.6) which is kind of odd for problems of this nature. You usually will get a nice round number. So the first assumption that they are vertical angles is probably correct in which case the mistake in the problem is saying RQS and TQS are vertical angles instead of RQS and TQU. Bring this to your teacher's attention and see what the teacher says.