1. help with bisectors.

this is the figure:

and these are the questions:

Line segment TO is the bisector of <GTA and <GTA is a right <; m<GTO = (5x)deg, and m<OTA = (3x+10)deg
1. What is x?
2. What is m<GTO? if m<ATG = (4x-12)deg and m<GTO = 24
3. What is x?
4. What is m<ATG if m<ATG = (5x+18)deg, m<ATO = (2x+12)deg
5. Find <GTO

an explanation on how to get will help me so much.. thank you..

2. Re: help with bisectors.

Originally Posted by heycow123

this is the figure:

and these are the questions:

Line segment TO is the bisector of <GTA and <GTA is a right <; m<GTO = (5x)deg, and m<OTA = (3x+10)deg
1. What is x?
2. What is m<GTO? if m<ATG = (4x-12)deg and m<GTO = 24
3. What is x?
4. What is m<ATG if m<ATG = (5x+18)deg, m<ATO = (2x+12)deg
5. Find <GTO

an explanation on how to get will help me so much.. thank you..
If OT is an angle bisector, then wouldn't that mean that \displaystyle \displaystyle \begin{align*} \angle GTO = \angle OTA \end{align*}? From here we get \displaystyle \displaystyle \begin{align*} 5x = 3x + 10 \end{align*}. Solve for x.

3. Re: help with bisectors.

if TO is the bisector of <GTA, and <GTO = 5X and <OTA = 3X+10 it is not possible to say that <GTA is a right angle. There are too many constraints that do not make sense.
As "Prove it" mentioned, the angles have to be equal if they are the result of bisecting another angle. Therefore X=5 and <GTA must be:
5X+3X+10 = 8X +10 = 50
Are you sure you got your question and the values/wording correct....otherwise it is just a contradiction?
The other way to think of it is if GTA is a right angle, then the bisect will be 45 deg. This then makes X either 7 deg or 11.7 deg, which also doesn't make sense!
Maybe it will help to post a picture of the complete question instead of the diagram if possible.