Question

Need geometry help

Answer 1

Read Euclid.

Answer 2

\[\angle RQS \] and \[\angle TQS\] are a linear pair where \[m \angle RQS=2x+4\] and \[m \angle TQS=6x+20\]

1. Solve for x.
2. FInd \[m \angle RQS\] and \[m \angle TQS\]
3. Show how you can check your answer.

Answer 3

if two angles x and y are a linear pair, then they are adjacent and supplementary

so that means they add to 180 degrees

ie

x+y = 180

Answer 4

in this case, RQS and TQS are a linear pair, so that means


(2x+4) + (6x+20) = 180


solve for x

Answer 5

tell me what you get

Answer 6

x=19.5?

Answer 7

now use this to find angles RQS and TQS

Answer 8

I'll do the first angle to show you what I mean

Answer 9

angle RQS=2x+4

angle RQS=2*19.5+4 ... replace x with 19.5 (since x = 19.5)

angle RQS=39+4

angle RQS=43 degrees

Answer 10

I tried to do the one for angle TQS and this is what i got:

angle TQS=6x+20

angle TQS=6*19.5+20

angle TQS=117+20

angle TQS=119 degrees

Answer 11

did i do it correct?

Answer 12

117 + 20 is NOT equal to 119

Answer 13

I can see how you got 119, you did 117+2

Answer 14

137 sorry

Answer 15

you got it

Answer 16

the check is to make sure they add to 180, and they do

(angle RQS) + (angle TQS)

(43) + (137)

43 + 137

180

so that checks out

Answer 17

Thank you for helping me :)

Would you be able to guide me thru another question similar to what we just did?

Answer 18

sure I can do one more

Answer 19

Ok, great! :-)



\[\angle RQS\] and \[\angle TQS \] are vertical angles where \[m \angle RQS=3(x+7) \] and \[m \angle TQS=4x+15\]


1. Solve for x.
2. Find \[m \angle RQS\] and \[m \angle TQS \]
3. Show how you can check your answer.

Answer 20

hint: vertical angles are congruent

Answer 21

would you be able to help me find x?

Answer 22

angle RQS = angle TQS

3(x+7) = 4x+15

3x + 21 = 4x + 15

solve for x

Answer 23

would x be 6?

Answer 24

correct

Answer 25

now use this to find angle RQS and angle TQS

Answer 26

angle RQS=3(x+7)

angle RQS=3*6+7

angle RQS=18+7

angle RQS=25 degrees


angle TQS=4x+15

angle TQS=4*6+15

angle TQS=24+15

angle TQS=39 degrees

Answer 27

angle RQS=3(x+7)

angle RQS=3(6+7)

angle RQS=3(13)

angle RQS=39

Answer 28

TQS is correct

Answer 29

Thank you so much for your help :)

Answer 30

you're welcome