if NS bisects

Question

if NS bisects <QNR, find m<QNR
QNS is (6x-57)
RNS is (2x+ 15)

anonymous · Answer

I forgot how to do this. do I add the x and the subtact 15 from each side

tkhunny · Answer

Did you draw a picture?

anonymous · Answer

Yes

tkhunny · Answer

Did you see that angles QNS and RNS are a linear pair?

anonymous · Answer

yes

tkhunny · Answer

Trick question.  You should not see that because we are not told that.|dw:1441039192569:dw|

Definition of bisector.  What can we say about the measures of the two angles created by the bisection?

anonymous · Answer

Haha good one, and I have no clue.

tkhunny · Answer

"BI"  What might that mean?

tkhunny · Answer

Bimonthly
Bicycle
Bifurcate
Bisect

anonymous · Answer

bisect

tkhunny · Answer

Right.  And what does "bi" mean in this case?

anonymous · Answer

dived into two parts

tkhunny · Answer

Two EQUAL parts.  The measures of the two angles are equal.

Now what?  We are given the measures of the two angles.

anonymous · Answer

Yes. (2x+15) and (6x-15)

tkhunny · Answer

It says "57" above.  Which is correct.

Anyway, you are nearly done.

2x+15 = 6x-15

Solve or x.  This will not quite complete the assignment.

anonymous · Answer

So I add 6x and 2x and I get 8x. or do I subtract them???

tkhunny · Answer

No.  You must solve using normal procedures.  Don't get jumpy.

Subtract 2x from both sides.

anonymous · Answer

how do you know if you subtract or add

tkhunny · Answer

You need to create zeros.

2x +15 = 6x - 15

Subtract 2x

2x - 2x +15 = 6x - 2x - 15

0 +15 = 4x - 15

Or just

15 = 4x - 15

Now, add 15.  It should create zero, somewhere.

anonymous · Answer

yes I got that

anonymous · Answer

then aren't you left with 4x

tkhunny · Answer

You must be more careful.

15 = 4x - 15

Add 15

15 + 15 = 4x - 15 + 15

30 = 4x - 0

30 = 4x

Now, divide by 4.  Be careful.