Question

Hi I need help with this portfolio, I did the rest but I forgot how to find x, please someone explain: ∠ RQS and ∠ TQS are a linear pair where m∠ RQS = 2x + 4 and m∠ TQS = 6x + 20 Thank you!

Answer 1

Linear pairs are supplementary.

Answer 2

@SACAPUNTAS I know what linear pair are I need help to find x, because I've been out of country for a month and forgot how to do that and my teacher isn't picking up his phone

Answer 3

You have two values. You know they add up to 180. Write the equation.

Answer 4

like (2x+4) + (6x+20)=180? or 360?

Answer 5

You tell me. Do they add up to 180, or to 360?

Answer 6

If linear pair is supplementary then they probably add up to 360?

Answer 7

No.

Supplementary angles add up to 180. The two angles you are given are supplementary angles. So they add up to 180.
\[(2x + 4) + (6x + 2) = 180\]
Don't be fooled by the angles themselves being given as something plus something else. That's still just one angle, so you're adding two angles, not four. The sum is still 180.

Answer 8

(6x + 20) rather.

Answer 9

oh I see now, so the next step would be
(2x + 6x)+(4+20)=180? combine like terms?

Answer 10

Yes!

Answer 11

so it would be then 8x+24=180?

Answer 12

So far so good. Keep going.

Answer 13

then I get to add 24 to each side? 8x=186? or do I subscribe?

Answer 14

It's 8x + 24 = 180.
You're trying to get rid of that extra 24. So subtract 24 from both sides of the equation.
\[8x + 24 = 180 \\ 8x + 24 - 24 = 180 - 24 \\ 8x = 156\]

Answer 15

ah thats how it is I've been breaking my head thinking that I can't exceed 180 if its supplementary and was afraid to ask and now I that I did I understand better lol
now I all gotta to do is divide each by 8 which will be x=19.5 ?

Answer 16

Correct.

Also, you should remember that there's nothing saying the right side of the equation won't exceed 180 due to whatever algebraic manipulations needed to solve it. The laws of geometry are no longer important once you've started crunching the numbers.

Answer 17

For example, if I had two supplementary angles that were 0.1x and 0.05x you would certainly exceed 180 when finding x. But no rules of geometry are being broken.

Answer 18

Oh I see I haven't gotten to that part of geometry yet but I will and thank you for heads up ;)

Answer 19

are you will be available to help with other math problems even if I'm not in Connections? just problems from public school book?

Answer 20

Yeah, I'm not in Connections either.

Answer 21

Thank you so much some ppl just give answers I don't need that I need to know the steps and explanations...thanks again! ;)

Answer 22

@SACAPUNTAS I've got another problem and can you read it and tell me if its the same steps as previous? seems like this one is without parenthesis.
∠ RQS and ∠ TQS are vertical angles where m∠ RQS = 3(x + 7) and m∠ TQS = 4x + 15.

Answer 23

This one is slightly different. Vertical angles are equal.

Answer 24

then how do I solve the x because all I see is 4x and just x?

Answer 25

You're given two values, and they are equal. You can write the equation.

Answer 26

if I solve one equation the other is equal? or what should be my first step?