+0  
 
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avatar+81 

Hello,

 

I was looking through some old questions.

 

I do not understand this one, and I was wondering if anyone could help me.

https://web2.0calc.com/questions/parallel-lines-and-triangle

 

Thank you so much in advance!!!

 Mar 23, 2021
 #1
avatar+148 
+2

on the original post, Melody has given some great hints. i hope you can learn to understand them better in the future!

 

well, following Melody's hints, we can solve the problem (the steps in bold were not by me, they were by Melody):

 

1) find angle PST in terms of x                           180-(2x+8)      

 

2) Find angle PTS in terms of x                            x

 

3)  Solve for x                                                       we get this equation: 40 + x + 180 - 2x - 8 = 180  (this is because all angles in a triangle sum up to 180).

                                                                               212 - x = 180

                                                                               - x = -32

                                                                               x = 32

 

4)  Determine STR                                                angle STR is on the same line as angle PTS, which is simply just x. so angle STR is 180 - 32, which is 148 degrees.

 

 

hope this helped! please let me know if you have any follow-up questions smiley

 Mar 24, 2021
edited by idyllic  Mar 24, 2021
 #4
avatar+81 
+1

Thank you so much, that is correct!

TheMathWhiz  Mar 24, 2021
 #3
avatar
+1

In the diagram below, we have ST || QR, ∠P = 40º, and ∠QST = 2∠R + 8º. Find the measure of ∠STR in degrees.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We can find the measure of angle R by using this equation:

 

180 - (2R + 8) + R + 40 = 180

 

∠R = 32º

 

∠STR = 180 - ∠R = 148º

 Mar 24, 2021

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