 B H.

# Angles in a Triangle

Given a triangle RST and point U on line RT, line segment RS is congruent to line segment ST. The measure of angle RST is 3x-48 and the measure of angle STU is 9x. Solve for x.

<a href="https://ibb.co/rHWJF4f"><img src="https://i.ibb.co/rHWJF4f/Impossible-Triangle-Question2.png" alt="Impossible-Triangle-Question2" border="0"></a>

This was an actual question on my son's 9th grade Geometry test. It looks like there is a typo somewhere because I'm 95% sure there is no solution.

Brenda D.

tutor
I think you are probably correct since Triangle RST must total 180 degrees. The variable, x can be found by setting the measure of RST equal to 180, the resulting value for x checks for RST but not for STU, with RS=ST per the information given. I could not get the link to yield a picture or diagram.
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10/28/20

By:

Tutor
5 (5)

Experienced Geometry Tutor

B H.

I guess my diagram didn't post on there. None of the angles in the triangle can have a measure of 9x. STU is 'outside' of the triangle. So angles SRT and STR are congruent and have a measure of 180 - 9x. I can solve for x (180 - 9x + 180 - 9x + 3x - 48 = 180) and get x = 8.8. But that would mean the measure of angle RST is negative, since RST = 3x - 48.
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10/29/20 Vidya V.

tutor
Ok. Yes I didn’t see the diagram and thought U was a point on the segment RT. Now I see your point. I am also confused? Please post the answer if there is one! Thank you.
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10/29/20

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