Obtuse triangle, bisected, RTU=11x-30, TRS=13x-32, RUS=94

[carlasap]

Please help me. I'm trying to help my daughter with Geometry and it's been a while for me.
She is trying to solve find the measurement of an angle.

Obtuse triangle. Bisected. We are given the following info:
RTU=11x-30, TRS=13x-32, and RUS=94. Find m of RSU. RU is the angle bisector.

R is top point, T is bottom left and S is bottom right. Again, RU is angle bisector. I know this may seem stupid, but now I'm determined to figure this out, hopefully with your help.
Thanks,

 

[Loren]

Re: Trying to help daughter

angle RTU=11x-30
angle TUR=180°-94° = 86°
angle TRU = (1/2)(13x-32)
angle RTU + angle TUR + angle TRU = 180°.

 

[carlasap]

Re: Trying to help daughter

Thanks so much. I hope this helps her.

 

[carlasap]

Re: Trying to help daughter

Hi Loren, it's me again. If I worked this right x=7.5. That adds up to 188. Am I forgetting something? Remember, it's been 25 years!!!

 

[chivox]

Re: Trying to help daughter

Hi Loren, it's me again. If I worked this right x=7.5. That adds up to 188. Am I forgetting something? Remember, it's been 25 years!!!

No problem... The approach is right (set the sum of the angles of a triangle equal to 180 and solve for x). If it doesn't work when you plug x back in to check your work, it's just a computation error of some sort. Here's my work, so just compare it with yours, and the error should jump out. Let m = mRSU. Then for the big triangle TRS, we have

\(\displaystyle (11 x - 30) + (13 x - 32) + m = 180\)

But we also know from one of the little triangles RUS,

\(\displaystyle \frac{1}{2} (13 x - 32) + 94 + m = 180\)

Since both of those equal 180, we can equate them and solve

\(\displaystyle \frac{1}{2} (13 x - 32) + 94 + m = (11 x - 30) + (13 x - 32) + m\)

Eliminate m and combine like terms...

\(\displaystyle \frac{13}{2} x - 16 + 94 = 11 x + 13 x - 30 - 32\)

\(\displaystyle \frac{13}{2} x + 78 = 24 x - 62\)

\(\displaystyle 140 = \frac{35}{2} x\)

\(\displaystyle x = 8\)

Then, substitute that back in for mTRS, mSTR, and subtract from 180... It should be all right, although your daughter should check the work, not me. The answer for mRSU should be 50 degrees.

-Paul